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Applicable Analysis
An International Journal
Volume 78, 2001 - Issue 3-4
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Original Articles

Inverse scattering solutions of the hunter-saxton equation

Hunter-saxton equation

Richard Beals Yale University, New Haven, 06520, Connecticut
,
David H. Sattinger Yale University, New Haven, 06520, Connecticut
&
Jacek Szmigielski Yale University, New Haven, 06520, Connecticut
Pages 255-269 | Received 11 Nov 2000, Published online: 23 Jun 2010

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Xiangke Chang & Jacek Szmigielski. (2016) Lax Integrability of the Modified Camassa-Holm Equation and the Concept of Peakons. Journal of Nonlinear Mathematical Physics 23:4, pages 563-572.
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Yu Hou & Engui Fan. (2014) Algebro-geometric solutions for the two-component Hunter-Saxton hierarchy. Journal of Nonlinear Mathematical Physics 21:4, pages 473-508.
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XUEMEI WEI & ZHAOYANG YIN. (2011) GLOBAL EXISTENCE AND BLOW-UP PHENOMENA FOR THE PERIODIC HUNTER–SAXTON EQUATION WITH WEAK DISSIPATION. Journal of Nonlinear Mathematical Physics 18:1, pages 139-149.
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Hans Lundmark & Jacek Szmigielski. (2008) Continuous and Discontinuous Piecewise Linear Solutions of the Linearly Forced Inviscid Burgers Equation. Journal of Nonlinear Mathematical Physics 15:sup3, pages 264-276.
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Articles from other publishers (77)

Yingying Guo, Weikui Ye & Zhaoyang Yin. (2024) Sharp ill-posedness for the Hunter–Saxton equation on the line. Journal of Evolution Equations 24:2.
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Thomas Christiansen, Katrin Grunert, Anders Nordli & Susanne Solem. (2024) A Convergent Numerical Algorithm for $$\alpha $$-Dissipative Solutions of the Hunter–Saxton Equation. Journal of Scientific Computing 99:1.
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Qiulan Zhao, Huanjin Wang & Xinyue Li. (2023) Novel symmetric structures and explicit solutions to a coupled Hunter-Saxton equation. Physica Scripta 98:6, pages 065212.
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Albert Ai & Ovidiu-Neculai Avadanei. (2023) Well-Posedness for the Dispersive Hunter–Saxton Equation. International Mathematics Research Notices 2023:9, pages 7883-7924.
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Shao-Wen Yao, Selahattin Gulsen, M.S. Hashemi, Mustafa Inc & Harun Bicer. (2023) Periodic Hunter–Saxton equation parametrized by the speed of the Galilean frame: Its new solutions, Nucci’s reduction, first integrals and Lie symmetry reduction. Results in Physics 47, pages 106370.
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Oleg Morozov. 2023. The Diverse World of PDEs. The Diverse World of PDEs 215 229 .
Denis Blackmore, Yarema Prykarpatsky, Mykola M. Prytula, Denys Dutykh & Anatolij K. Prykarpatski. (2022) On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries. Analysis and Mathematical Physics 12:2.
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Bo Jiang. (2022) A Blow-up Result for the Periodic Solutions to an Integrable Dispersive Hunter–Saxton Equation. Journal of Nonlinear Mathematical Physics 29:1, pages 115-123.
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Weikui Ye & Zhaoyang Yin. (2022) Global Existence and Blow-Up Phenomena for the Hunter-Saxton Equation on the Line. Journal of Mathematical Fluid Mechanics 24:1.
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Ashish Kumar Rawat, Neeraj Dhiman & Anand Chauhan. Numerical treatment of Hunter Saxtan equation by spline function. Numerical treatment of Hunter Saxtan equation by spline function.
Manish Goyal & Haci Mehmet Baskonus. (2021) A Reliable Solution of Arbitrary Order Nonlinear Hunter–Saxton Equation with Time Dependent Derivative in Liouville–Caputo Sense. International Journal of Applied and Computational Mathematics 7:4.
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Iftikhar Ahmad, Hira Ilyas, Kadir Kutlu, Vizda Anam, Syed Ibrar Hussain & Juan Luis García Guirao. (2021) Numerical computing approach for solving Hunter-Saxton equation arising in liquid crystal model through sinc collocation method. Heliyon 7:7, pages e07600.
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Oleg I. Morozov. (2021) Integrability structures of the generalized Hunter–Saxton equation. Analysis and Mathematical Physics 11:2.
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Chunyu Shen & Yaqi Tian. (2021) Global asymptotic stabilization of the Hunter-Saxton control system. European Journal of Control 59, pages 129-136.
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Aly R. Seadawy, Syed Tahir Raza Rizvi, Sarfraz Ahmad, Muhammad Younis & Dumitru Baleanu. (2021) Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Physics 19:1, pages 1-10.
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Changzheng Qu & Ying Fu. (2019) On the Cauchy problem and peakons of a two-component Novikov system. Science China Mathematics 63:10, pages 1965-1996.
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Weikui Ye & Zhaoyang Yin. (2019) Global existence for the periodic dispersive Hunter–Saxton equation. Monatshefte für Mathematik 191:2, pages 267-278.
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Yingying Guo & Zhaoyang Yin. (2019) Local well-posedness and blow-up phenomena of the generalized short pulse equation. Journal of Mathematical Physics 60:4.
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Weiguo Rui. (2018) Idea of invariant subspace combined with elementary integral method for investigating exact solutions of time-fractional NPDEs. Applied Mathematics and Computation 339, pages 158-171.
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Feng Wang, Fengquan Li & Zhijun Qiao. (2018) Well-posedness and peakons for a higher-order -Camassa–Holm equation . Nonlinear Analysis 175, pages 210-236.
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Zhang Mengxia & Yang Xiaomin. (2018) A Synthetical Two-Component Model with Peakon Solutions: One More Bi-Hamiltonian Case. Zeitschrift für Naturforschung A 73:5, pages 425-430.
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Chunyu Shen. (2018) Optimal solution and optimality condition of the Hunter-Saxton equation. Journal of Mathematical Physics 59:2.
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Min Li & Zhaoyang Yin. (2017) Global existence and local well-posedness of the single-cycle pulse equation. Journal of Mathematical Physics 58:10.
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Ying Fu & Changzheng Qu. (2017) Well-posedness and wave breaking of the degenerate Novikov equation. Journal of Differential Equations 263:8, pages 4634-4657.
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Kourosh Parand & Mehdi Delkhosh. (2017) An Efficient Numerical Solution of Nonlinear Hunter–Saxton Equation. Communications in Theoretical Physics 67:5, pages 483.
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Min Li & Zhaoyang Yin. (2017) Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation. Discrete & Continuous Dynamical Systems - A 37:12, pages 6471-6485.
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Kale Colville, Daniel Gomez & Jacek Szmigielski. (2016) On Isospectral Deformations of an Inhomogeneous String. Communications in Mathematical Physics 348:3, pages 771-802.
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Jingqun Wang, Lixin Tian & Weiwei Guo. (2016) Global exact controllability and asympotic stabilization of the periodic two-component $\mu\rho$-Hunter-Saxton system. Discrete and Continuous Dynamical Systems - Series S 9:6, pages 2129-2148.
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Yongsheng Mi, Chunlai Mu & Pan Zheng. (2016) On the Cauchy problem of the modified Hunter-Saxton equation. Discrete and Continuous Dynamical Systems - Series S 9:6, pages 2047-2072.
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Feng Wang, Fengquan Li & Qiaoling Chen. (2015) On the Cauchy problem for a weakly dissipative generalized $$\mu $$ μ -Hunter-Saxton equation. Monatshefte für Mathematik 181:3, pages 715-744.
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Xiang-Ke Chang, Xing-Biao Hu & Jacek Szmigielski. (2016) Multipeakons of a two-component modified Camassa–Holm equation and the relation with the finite Kac–van Moerbeke lattice. Advances in Mathematics 299, pages 1-35.
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Somayeh Arbabi, Akbar Nazari & Mohammad Taghi Darvishi. (2016) A semi-analytical solution of Hunter–Saxton equation. Optik 127:13, pages 5255-5258.
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Hong-Liu Cai & Chang-Zheng Qu. (2016) Integrability and Solutions of the (2 + 1)-dimensional Hunter–Saxton Equation. Communications in Theoretical Physics 65:4, pages 397-404.
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Kai Tian & Q P Liu. (2016) Conservation laws and symmetries of Hunter–Saxton equation: revisited. Nonlinearity 29:3, pages 737-755.
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Abdon Atangana, Dumitru Baleanu & Ahmed Alsaedi. (2016) Analysis of time-fractional hunter-saxton equation: a model of neumatic liquid crystal. Open Physics 14:1, pages 145-149.
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Yongsheng Mi & Chunlai Mu. (2014) Well‐posedness for the Cauchy problem of the modified Hunter–Saxton equation in the Besov spaces. Mathematical Methods in the Applied Sciences 38:17, pages 4061-4074.
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Mathew Baxter, Robert A. Van Gorder & Kuppalapalle Vajravelu. (2015) Several Types of Similarity Solutions for the Hunter–Saxton Equation*. Communications in Theoretical Physics 63:6, pages 675-681.
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Feng Wang, Fengquan Li & Qiaoling Chen. (2015) Wave breaking and global existence for a weakly dissipative generalized two-component -Hunter–Saxton system . Nonlinear Analysis: Real World Applications 23, pages 61-77.
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Byungsoo Moon. (2015) ANALYTIC SOLUTIONS OF THE CAUCHY PROBLEM FOR THE GENERALIZED TWO-COMPONENT HUNTER-SAXTON SYSTEM. Honam Mathematical Journal 37:1, pages 99-112.
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Alejandro Sarria. (2015) Global estimates and blow-up criteria for the generalized Hunter-Saxton system. Discrete and Continuous Dynamical Systems - Series B 20:2, pages 641-673.
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Xiangke Chang, Xiaomin Chen & Xingbiao Hu. (2014) A generalized nonisospectral Camassa–Holm equation and its multipeakon solutions. Advances in Mathematics 263, pages 154-177.
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Yu Hou, Engui Fan & Peng Zhao. (2013) Algebro-geometric solutions for the Hunter–Saxton hierarchy. Zeitschrift für angewandte Mathematik und Physik 65:3, pages 487-520.
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RAFAEL HERNÁNDEZ HEREDERO & ENRIQUE G. REYES. (2013) NONLOCAL SYMMETRIES, COMPACTON EQUATIONS, AND INTEGRABILITY. International Journal of Geometric Methods in Modern Physics 10:09, pages 1350046.
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Byungsoo Moon. (2013) Solitary wave solutions of the generalized two-component Hunter–Saxton system. Nonlinear Analysis: Theory, Methods & Applications 89, pages 242-249.
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Ling Zhang & Dafeng Zuo. (2013) Two supersymmetric hierarchies related to the super-HS spectral problem. Communications in Nonlinear Science and Numerical Simulation 18:2, pages 257-263.
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Jianmei Zhang & Lixin Tian. (2013) Wave-Breaking Criterion for the Generalized Weakly Dissipative Periodic Two-Component Hunter-Saxton System. Journal of Applied Mathematics 2013, pages 1-10.
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Ying Zhang, Yue Liu & Changzheng Qu. (2013) Blow up of Solutions and Traveling Waves to the Two-Component μ-Camassa–Holm System. International Mathematics Research Notices 2013:15, pages 3386-3419.
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Jingjing Liu & Zhaoyang Yin. (2011) Global weak solutions for a periodic two-component μ-Hunter–Saxton system. Monatshefte für Mathematik 168:3-4, pages 503-521.
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Przemysław Górka & Enrique G. Reyes. (2012) The modified Hunter–Saxton equation. Journal of Geometry and Physics 62:8, pages 1793-1809.
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Xuemei Wei. (2012) Global weak solution for a periodic generalized Hunter–Saxton equation. Journal of Mathematical Analysis and Applications 391:2, pages 530-543.
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Jingjing Liu & Zhaoyang Yin. (2012) On the Cauchy problem of a periodic 2-component -Hunter–Saxton system. Nonlinear Analysis: Theory, Methods & Applications 75:1, pages 131-142.
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Xuemei Wei & Zhaoyang Yin. (2011) Global existence and blow-up phenomena for the periodic Hunter–Saxton equation parametrized by the speed of the Galilean frame. Nonlinear Analysis: Real World Applications 12:5, pages 2616-2624.
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