Novel homoclinic and heteroclinic solutions for the 2D complex cubic Ginzburg-Landau equation

DOI10.1016/j.physleta.2009.10.069zbMath1235.35267OpenAlexW2135862943MaRDI QIDQ763821

Zhengde Dai, Mingming Leng, Jian Huang

Publication date: 2 April 2012

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2009.10.069

zbMATH Keywords

heteroclinic orbitshomoclinic orbitslinearized stability2D cubic Ginzburg-Landau equationHirota's bilinear transformationhyperbolic property

Mathematics Subject Classification ID

Homoclinic and heteroclinic orbits for dynamical systems (37C29) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Soliton solutions (35C08) Ginzburg-Landau equations (35Q56)

Related Items (1)

Effect of near  -symmetric potentials on nonlinear modes for higher-order generalized Ginzburg–Landau model

Cites Work

• Exact homoclinic wave and soliton solutions for the 2D Ginzburg-Landau equation
• Homoclinic breather-wave solutions for sine-Gordon equation
• Bifurcations and competing coherent structures in the cubic-quintic Ginzburg--Landau equation. I: Plane wave (CW) solutions
• Explicit homoclinic tube solutions and chaos for Zakharov system with periodic boundary
• Smale horseshoes and symbolic dynamics in perturbed nonlinear Schrödinger equations
• Periodic wave solutions to a coupled KdV equations with variable coefficients
• Variational principles for Ginzburg-Landau equation by He's semi-inverse method
• Homoclinic solutions for Davey-Stewartson equation
• Exact solutions of generalized Zakharov and Ginzburg-Landau equations
• Homoclinic orbits for the coupled nonlinear Schrödinger system and long-short wave equation
• Homoclinic orbits and periodic solitons for Boussinesq equation with even constraint
• Traveling wavetrains in the complex cubic-quintic Ginzburg-Landau equation
• Homoclinic orbits for the perturbed sine-Gordon equation
• Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation

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