Evolution of nonsoliton and ``quasi-classical wavetrains in nonlinear Schrödinger and Korteweg-de Vries equations with dissipative perturbations

DOI10.1016/0167-2789(87)90052-2zbMath0635.35082OpenAlexW2046779143MaRDI QIDQ1097417

Boris A. Malomed

Publication date: 1987

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(87)90052-2

zbMATH Keywords

inverse scattering transformexplicit solutionssolitonsattractionKorteweg-de Vries equationrepulsioneikonal approximationwavetrainnonlinear superpositionquasi-classicalNonlinear Schrödinger equationsdissipative perturbationdissipationslinear instability thresholdlogarithmic approximationnon-solitonsoliton- birth threshold

Mathematics Subject Classification ID

Perturbation theories for operators and differential equations in quantum theory (81Q15) Perturbations in context of PDEs (35B20) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items

𝒫𝒯-symmetric and antisymmetric nonlinear states in a split potential box, Solitary waves under the influence of a long-wave mode, Nonlinear Schrödinger equations within the Nelson quantization picture., Modulational instability in linearly coupled complex cubic-quintic Ginzburg-Landau equations, On the forced nonlinear Schrödinger equation, Ginzburg-Landau models of nonlinear electric transmission networks, Multidimensional dissipative solitons and solitary vortices, Solitons in ${\mathscr{P}}{\mathscr{T}}$-symmetric ladders of optical waveguides, Dissipative light bullets: from stationary light bullets to double, quadruple, sixfold, eightfold and tenfold bullet complexes, Mutual transitions between stationary and moving dissipative solitons, The cubic complex Ginzburg-Landau equation for a backward bifurcation, Exact solutions in nonlinearly coupled cubic-quintic complex Ginzburg-Landau equations, Gauge equivalence among quantum nonlinear many body systems, Fronts, pulses, sources and sinks in generalized complex Ginzburg-Landau equations, Manakov model with gain/loss terms and \(N\)-soliton interactions: effects of periodic potentials, On the generation of dispersive shock waves, Erupting, flat-top, and composite spiral solitons in the two-dimensional Ginzburg-Landau equation, Stable localized pulses and zigzag stripes in a two-dimensional diffractive-diffusive Ginzburg-Landau equation, Motion of pulses and vortices in the cubic-quintic complex Ginzburg-Landau equation without viscosity, Solitary pulses in linearly coupled Ginzburg-Landau equations, Stable autosolitons in dispersive media with saturable gain and absorption, Breathing and randomly walking pulses in a semilinear Ginzburg-Landau system, Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations

Cites Work

• Unnamed Item
• Unnamed Item
• Asymptotic solutions of nonlinear evolution equations and a Painlevé transcedent
• Exact and numerical solutions to the perturbed sine-Gordon equation
• Convection patterns in large aspect ratio systems
• Quantum field theory techniques in graphical enumeration
• Nonlinear Schrödinger equation including growth and damping
• Nonlinear tunnelling
• Stability of Spatially Periodic Supercritical Flows in Hydrodynamics
• A non-linear instability theory for a wave system in plane Poiseuille flow