# Solitary waves for a class of quasilinear SchrÃ¶dinger equations in dimension two

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We obtain exact spatiotemporal periodic traveling wave solutions to the generalized (3+1)-dimensional cubic-quintic nonlinear SchrÃ¶dinger equation with spatial distributed coefficients. For restrictive parameters, these periodic wave solutions acquire the form of localized spatial solitons....

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The SchrÃ¶dinger-KdV equation with power-law nonlinearity is studied in this paper. The solitary wave ansatz method is used to carry out the integration of the equation and obtain one-soliton solution. The Gâ€²/ G method is also used to integrate this equation. Subsequently, the...

- ELLIPTIC EQUATIONS WITH MEASURE DATA IN ORLICZ SPACES. GE DONG // Electronic Journal of Differential Equations;2008, Vol. 2008, Special section p1
This article shows the existence of solutions to the nonlinear elliptic problem A(u) = f in Orlicz-Sobolev spaces with a measure valued right- and side, where A(u) = -div a(x, u, âˆ‡u) is a Leray-Lions operator defined on a subset of W0 Â¹ LM(Î©), with general M.

- GLOBAL BRANCH OF SOLUTIONS FOR NON-LINEAR SCHRÃ–DINGER EQUATIONS WITH DEEPENING POTENTIAL WELL. STUART, C. A.; ZHOU, HUAN-SONG // Proceedings of the London Mathematical Society;May2006, Vol. 92 Issue 3, p655
We>0$ and the functions $f$ and $g$ are such that\begin{equation*} \lim_{s \rightarrow 0}\frac{f(s)}{s} = 0 \mbox{and} 1 \alpha + 1 = \lim _{|s| \rightarrow \infty}\frac{f(s)}{s} \infty\end{equation*} and \begin{equation*} g(x)\equiv 0 \mbox{on} \bar{\Omega}, g(x)\in (0, 1] \mbox{on}...

- EXISTENCE AND MULTIPLICITY OF SEMICLASSICAL STATES FOR A QUASILINEAR SCHRÃ–DINGER EQUATION IN Râ„N. MINBO YANG; YANHENG DING // Communications on Pure & Applied Analysis;Jan2013, Vol. 12 Issue 1, p429
In this paper we consider the following modified version of nonlinear SchrÃ¶dinger equation: -ÎµÂ² Î”u+V(x)u-ÎµÂ²Î”(uÂ²)u=g(x,u) in , âˆN, N Îµ 3 and g(x, u) is a superlinear but subcritical function. Apply- R ing variational methods we show the existence and multiplicity...

- GROUND STATE SOLUTIONS FOR QUASILINEAR STATIONARY SCHRODINGER EQUATIONS WITH CRITICAL GROWTH. SOUTO, MARCO A. S.; SOARES, SÉRGIO H. M. // Communications on Pure & Applied Analysis;Jan2013, Vol. 12 Issue 1, p99
We establish the existence of ground state solution for quasilinear SchrÃ¶dinger equations involving critical growth. The method used here is minimizing the gradient integral norm in a manifold defined by integrals involving the primitive of the nonlinearity function.

- Quasilinear Theory for the Nonlinear SchrÃ¶dinger Equation with Periodic Coefficients. Medvedev, S. B.; Fedoruk, M. P. // JETP Letters;1/10/2004, Vol. 79 Issue 1, p16
The nonlinear SchrÃ¶dinger equation with periodic coefficients is analyzed under the condition of large variation in the local dispersion. The solution after n periods is represented as the sum of the solution to the linear part of the nonlinear SchrÃ¶dinger equation and the nonlinear...

- Analytic presentation of a solution of the SchrÃ¶dinger equation. Liverts, E. Z.; Drukarev, E. G.; Krivec, R.; Mandelzweig, V. B. // Few-Body Systems;Dec2008, Vol. 44 Issue 1-4, p367
High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The SchrÃ¶dinger equation is cast into the nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The...

- Variable coefficient nonlinear SchrÃ¶dinger equations with four-dimensional symmetry groups and analysis of their solutions. Özemir, C.; Güngör, F. // Journal of Mathematical Physics;Sep2011, Vol. 52 Issue 9, p093702
Analytical solutions of variable coefficient nonlinear SchrÃ¶dinger equations having four-dimensional symmetry groups, which are in fact the next closest to the integrable ones occurring only when the Lie symmetry group is five-dimensional, are obtained using two different tools. The first...