References
- Borisov AB, Borovskii AV, Shiryaev OB, et al. Relativistic and charge-displacement self-channeling of intense ultrashort laser pulses in plasma. Phys Rev A. 1992;45(8):5830–5845.
- Borovskii AV, Galkin AL. Dynamial modulation of an ultrashort high-intensity laser pulse in matter. J Exp Theor Phys. 1993;77(4):562–573.
- Brandi H, Manus C, Mainfray G, et al. Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. Phys Fluids B. 1993;5:3539–3550.
- Chen XL, Sudan RN. Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma. Phys Rev Lett. 1993;70:2082–2085.
- Ritchie B. Relativistic self-focusing and channel formation in laser-plasma interactions. Phys Rev E. 1994;50(2):687–689.
- Sun GZ, Ott E, Lee YC, et al. Self-focusing of short intense pulses in plasmas. Phys Fluids. 1987;30(2):526–532.
- de Bouard A, Hayashi N, Saut JC. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Commun Math Phys. 1997;189:73–105.
- de Bouard A, Hayashi N, Naumkin PI, et al. Scattering problem and asymptotics for a relativistic nonlinear Schrödinger equation. Nonlinearity. 1998;12:1415–1425.
- Colin M. On the local well-posedness of quasilinear Schrödinger equations in arbitrary space dimension. Commun Part Diff Eqs. 2002;27:325–354.
- Colin M. Approximation of a quasilinear Schrödinger equation by a Klein–Gordon equation in space dimension 2. Asymptot Anal. 2003;34:275–309.
- Colin M. Stability of stationary waves for a quasilinear Schrödinger equation in dimension 2. Adv Diff Eqs. 2003;8(1):1–28.
- Wang YJ, Zhang YM. Positive solutions for a relativistic nonlinear Schrödinger equation with square-root nonlinearity. J Math Phys. 2020;61:Article ID 111509.
- Shen YT, Wang YJ. Soliton solutions for generalized quasilinear Schrödinger equations. Nonlinear Anal Theory Methods Appl. 2013;80:194–201.
- Cheng YK, Yang J. Positive solution to a class of relativistic nonlinear Schrödinger equation. J Math Anal Appl. 2014;411:665–674.
- Cheng YK, Yang J. The existence result for a relativistic nonlinear Schrödinger equation. J Math Phys. 2015;56(3):3262–3267.
- Cheng YK, Yao YX. Soliton solutions to a class of relativistic nonlinear Schrödinger equations. Appl Math Comput. 2015;260:342–350.
- Qiu W, Zhang YM, Abdelgadir AA. Existence of nontrivial solutions for a class of relativistic nonlinear Schrödinger equations. Acta Math Sci. 2019;39A:95–104.
- Deng YB, Peng SJ, Yan SS. Positive soliton solutions for generalized quasilinear Schrödinger equations with critical growth. J Differ Equ. 2015;258(1):115–147.
- Deng YB, Peng SJ, Yan SS. Critical exponents and solitary wave solutions for generalized quasilinear Schrödinger equations. J Differ Equ. 2016;260(2):1228–1262.
- Shen YT, Wang YJ. Standing waves for a class of quasilinear Schrödinger equations. Complex Var Elliptic Equ. 2016;61:817–842.
- Shen YT, Wang YJ. A class of generalized quasilinear Schrödinger equations. Commun Pure Appl Anal. 2016;15(3):853–870.
- Berestycki H, Lions PL. Nonlinear scalar field equations I. Arch Rational Mech Anal. 1983;82:313–346.
- Azzollini A, Pomponio A. On the Schrödinger equation in RN under the effect of a general nonlinear term. Indiana Univ Math J. 2009;58:1361–1378.
- Jeanjean L. On the existence of bounded Palais–Smale sequences and application to a Landesman-Lazer-type problem set on RN. Proc Roy Soc Edinb Sec A. 1999;129:787–809.
- Strauss WA. Existence of solitary waves in higher dimensions. Comm Math Phys. 1977;55:149–162.
- Alves CO, Wang YJ, Shen YT. Soliton solutions for a class of quasilinear Schrödinger equations with a parameter. J Differ Equ. 2015;259(1):318–343.
- Jeanjean L, Tanaka K. A remark on least energy solutions in RN. Proc Am Math Soc. 2003;131(8):2399–2408.