References
- M. J. Ablowitz, A. Ramani and H. Segur, Nonlinear evolution equations of Painlevé type, Lett. Nuovo Cim. 23 (1978) 333–338. doi: 10.1007/BF02824479
- M. J. Ablowitz and H. Segur, Solitons and the Inverse Scattering Transform (SIAM, 1981).
- A. A. Alexeyev, Superposition principles for nonlinear partial differential equations in (1+1) dimension, Abstract of Short Communications and Poster Sessions, ICM 1998 Int. Cong. of Mathematicians, Berlin, August 18-27 (Rosenheim: Geronimo GmbH, 1998) 227.
- A. A. Alexeyev, A multidimensional superposition principle: classical solitons I, Preprint (Karlsruhe University, Evolve-L Archive, 1999) 99-00010.
- A. A. Alexeyev, A multidimensional superposition and singular manifold expansions, Abstracts, 3rd European Congress In Mathematics, Barcelona, July 10-14, 2000 electronically/CD.
- A. A. Alexeyev, A multidimensional superposition principle: classical solitons I, Phys. Lett. A 278 (2001) 198–208. doi: 10.1016/S0375-9601(00)00775-1
- A. A. Alexeyev, Multidimensional superposition principle and invariant manifolds of soliton type, Abstracts, Workshop Computer Algebra in Applications to Integrable Systems November 16-17, 2001 (Cambridge, Isaac Newton Institute for Mathematical Sciences) electronically.
- A. A. Alexeyev, A multidimensional superposition principle: classical solitons II, J. Phys. A: Math. Gen. 36 (2003) 9843–9864. doi: 10.1088/0305-4470/36/38/303
- A. A. Alexeyev, A multidimensional superposition principle and waves switching in integrable and nonintegrable soliton models, J. Phys. A: Math. Gen. 37 (2004) L627–L634. doi: 10.1088/0305-4470/37/47/L01
- A. A. Alexeyev, A multidimensional superposition principle: classical solitons III, Phys. Lett. A 335 (2005) 197–206. doi: 10.1016/j.physleta.2004.12.011
- A. A. Alexeyev, A multidimensional superposition principle: numerical simulation and analysis of soliton invariant manifolds I, J. Nonl. Math. Phys. 14 (2007) 188–229. doi: 10.2991/jnmp.2007.14.2.5
- A. A. Alexeyev, Nonlinear waves in a fluid with ultra small bubbles, Abstracts of Papers, XXXII Conf. of the PhM and NS Faculty, Part 2 (Moscow: PFU Publishing, 1996), 53–54.
- A. A. Alexeyev, Classical and non-classical interactions of kinks in some bubbly mediums, J. Phys. A: Math. Gen. 32 (1999) 4419–4432. doi: 10.1088/0305-4470/32/24/307
- A. A. Alexeyev, Some notes on the singular manifold method: several manifolds and constraints, J. Phys. A: Math. Gen. 33 (2000) 1873–1894. doi: 10.1088/0305-4470/33/9/311
- S. C. Anco, N. T. Ngatat and M. Willoughby, Interaction properties of complex modified Kortewegde Vries (mKdV) solitons, Physica D 240 (2011) 1378–1394. doi: 10.1016/j.physd.2011.06.003
- R. Conte, Invariant Painlevé analysis of partial differential equations, Phys. Lett. A 140 (1989) 383–390. doi: 10.1016/0375-9601(89)90072-8
- B. A. Dubrovin and S. P. Novikov, Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory, Russ. Math. Surv. 44 (1989) 35–124. doi: 10.1070/RM1989v044n06ABEH002300
- P. G. Estévez et al, Modified singular manifold expansion: application to the Boussinesq and Mikhailov– Shabat systems, J. Phys. A: Math. Gen. 26 (1993) 1915–1925. doi: 10.1088/0305-4470/26/8/018
- J. D. Gibbon et al, Lax pairs Bäcklund transformations and special solutions for ordinary differential equations, Nonlinearity 1 (1988) 481–490. doi: 10.1088/0951-7715/1/3/005
- A. Heck, A birds-eye view of Gröbner bases, Nucl. Instrum. Methods A 389 (1997) 16–21. doi: 10.1016/S0168-9002(97)00032-6
- A. N. W. Hone and S. Lafortune, Stability of stationary solutions for nonintegrable peakon equations, Physica D 268 (2014) 28–36. doi: 10.1016/j.physd.2013.11.006
- Ch. K. R. T. Jones et al, On the stability analysis of periodic sine-Gordon traveling waves, Physica D 251 (2013) 63–74. doi: 10.1016/j.physd.2013.02.003
- T. Kawahara and M. Takaoka, Chaotic motions in an oscillatory soliton lattice, J. Phys. Soc. Japan 57 (1988) 3714–3732. doi: 10.1143/JPSJ.57.3714
- T. Kawahara and S. Toh, Pulse interactions in an unstable dissipative-dispersive nonlinear system, Phys. Fluids 31 (1988) 2103–2111. doi: 10.1063/1.866610
- A. P. Koller, Z. Hwang and M. Olshanii, Emergence of reflectionless scattering from linearizations of integrable PDEs around solitons, J. Phys. A: Math. Theor. 48 (2015) 075203. doi: 10.1088/1751-8113/48/7/075203
- W. X. Ma and B. Fuchssteiner, Integrable theory of the perturbation equations, Chaos Soliton. Fract. 7 (1996) 1227–1250. doi: 10.1016/0960-0779(95)00104-2
- E. L. Mansfield, Differential Gröbner bases, PhD Thesis (University of Sydney, 1992).
- M. Musette, R. Conte, The two-singular-manifold method: I. Modified Korteweg-de Vries and sine-Gordon equations, J. Phys. A: Math. Gen. 27 (1994) 3895–3913. doi: 10.1088/0305-4470/27/11/036
- A. Parker, On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave, Physica D 137 (2000) 25–33. doi: 10.1016/S0167-2789(99)00166-9
- A. Parker, On soliton solutions of the Kaup-Kupershmidt equation. II. Anomalous N-soliton solutions, Physica D 137 (2000) 34–48. doi: 10.1016/S0167-2789(99)00167-0
- J. Weiss, M. Tabor and G. Carneval, The Painlevé property for partial differential equations, J. Math. Phys. 24 (1983) 522–526. doi: 10.1063/1.525721
- A. D. Wittkopf and G. J. Reid, The “Rif” package and documentation, Maple 6 and higher (2000).
- T. Wolf and A. Brand, The Computer Algebra Package CRACK for Investigating PDEs, REDUCE User’s Manual, Version 3.7, A. C. Hearn and J. P. Fitch (Konrad-Zuze-Zentrum, 1999).