scholarly journals Existence of standing wave solutions for coupled quasilinear Schrödinger systems with critical exponents in ℝN

2017 ◽  
pp. 1-23
Author(s):  
Lili Wang ◽  
Xiangdong Fang ◽  
Zhi-Qing Han
Keyword(s):  
Standing Wave ◽  
Critical Exponents ◽  
Wave Solutions ◽  
Schrödinger Systems ◽  
Quasilinear Schrödinger Systems

scholarly journals New Types of Doubly Periodic Standing Wave Solutions for the Coupled Higgs Field Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Gui-qiong Xu
Keyword(s):  
Field Equation ◽  
Standing Wave ◽  
Higgs Field ◽  
Jacobi Elliptic Function ◽  
Bilinear Method ◽  
Wave Solutions ◽  
New Type ◽  
Function Expression ◽  
Parameter Values ◽  
Hirota Bilinear

Based on the Hirota bilinear method and theta function identities, we obtain a new type of doubly periodic standing wave solutions for a coupled Higgs field equation. The Jacobi elliptic function expression and long wave limits of the periodic solutions are also presented. By selecting appropriate parameter values, we analyze the interaction properties of periodic-periodic waves and periodic-solitary waves by some figures.

scholarly journals Instability of standing waves for non-linear Schrödinger-type equations

1988 ◽  
Vol 8 (8) ◽  
pp. 119-138 ◽  
Keyword(s):  
Dynamical Systems ◽  
Standing Wave ◽  
Optical Waveguides ◽  
Standing Waves ◽  
Positive Eigenvalue ◽  
Shooting Argument ◽  
Wave Solutions ◽  
Non Linear ◽  
Linearized Operator

AbstractA theorem is proved giving a condition under which certain standing wave solutions of non-linear Schrödinger-type equations are linearly unstable. The eigenvalue equations for the linearized operator at the standing wave can be analysed by dynamical systems methods. A positive eigenvalue is then shown to exist by means of a shooting argument in the space of Lagrangian planes. The theorem is applied to a situation arising in optical waveguides.

Some results on standing wave solutions for a class of quasilinear Schrödinger equations

2019 ◽  
Vol 60 (9) ◽  
pp. 091506 ◽  
Author(s):  
Jianhua Chen ◽  
Xianjiu Huang ◽  
Bitao Cheng ◽  
Chuanxi Zhu
Keyword(s):  
Standing Wave ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Wave Solutions
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