Soliton solutions for quasilinear Schrödinger equations, II

Abstract For a class of quasilinear Schrodinger equations, we establish the existence of ground states of soliton-type solutions by a variational method.

[1]  P. Rabinowitz,et al.  Dual variational methods in critical point theory and applications , 1973 .

[2]  W. Rother,et al.  Nonlinear scalar field equations , 1992, Differential and Integral Equations.

[3]  Pierre-Louis Lions,et al.  The concentration-compactness principle in the Calculus of Variations , 1985 .

[4]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[5]  Jiaquan Liu,et al.  Soliton solutions for quasilinear Schrödinger equations, I , 2002 .

[6]  Walter A. Strauss,et al.  Existence of solitary waves in higher dimensions , 1977 .

[7]  Thomas Bartsch,et al.  Existence and multiplicity results for some superlinear elliptic problems on RN , 1995 .

[8]  A. M. Sergeev,et al.  One-dimensional collapse of plasma waves , 1978 .

[9]  Alan Weinstein,et al.  Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential , 1986 .

[10]  Chen,et al.  Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse in underdense plasma. , 1993, Physical review letters.

[11]  Susumu Kurihara,et al.  Large-Amplitude Quasi-Solitons in Superfluid Films , 1981 .

[12]  P. Rabinowitz Minimax methods in critical point theory with applications to differential equations , 1986 .

[13]  L. Boccardo,et al.  Some remarks on critical point theory for nondifferentiable functionals , 1999 .

[14]  G. Bonnaud,et al.  Relativistic and ponderomotive self‐focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation , 1993 .

[15]  F. Bass Nonlinear electromagnetic-spin waves , 1990 .

[16]  Ritchie,et al.  Relativistic self-focusing and channel formation in laser-plasma interactions. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Pierre-Louis Lions,et al.  Nonlinear scalar field equations, I existence of a ground state , 1983 .

[18]  L. Boccardo,et al.  Critical points for multiple integrals of the calculus of variations , 1996 .

[19]  Marco Degiovanni,et al.  Deformation properties for continuous functionals and critical point theory , 1993 .

[20]  Miklos Porkolab,et al.  Upper‐hybrid solitons and oscillating‐two‐stream instabilities , 1976 .

[21]  A. Canino Multiplicity of solutions for quasilinear elliptic equations , 1995 .

[22]  Rainer W. Hasse,et al.  A general method for the solution of nonlinear soliton and kink Schrödinger equations , 1980 .

[23]  E. W. Laedke,et al.  Evolution theorem for a class of perturbed envelope soliton solutions , 1983 .

[24]  V. Makhankov,et al.  Non-linear effects in quasi-one-dimensional models of condensed matter theory , 1984 .

[25]  Akira Nakamura,et al.  Damping and Modification of Exciton Solitary Waves , 1977 .

[26]  S. Takeno,et al.  Classical Planar Heisenberg Ferromagnet, Complex Scalar Field and Nonlinear Excitations , 1981 .

[27]  Jean-Claude Saut,et al.  Global Existence of Small Solutions to a Relativistic Nonlinear Schrödinger Equation , 1997 .

[28]  P. Zweifel,et al.  Time‐dependent dissipation in nonlinear Schrödinger systems , 1995 .

[29]  G. Quispel,et al.  Equation of motion for the Heisenberg spin chain , 1981 .

[30]  F. Browder Variational methods for nonlinear elliptic eigenvalue problems , 1965 .