Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations

Gearhart-Prüss Theorem in stability for wave equations: a survey

We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney (regularized long-wave), Korteweg-deV...

The Eigenvalue Problem for Solitary Waves of the Green-Naghdi Equations

پایداری حلهای منفرد معادلات جفت شده غیر خطی شرودینگر مرتبه پنجم

  In this article we report the results of an investigation on the stability of solitary solutions to the Cubic-Quintic Coupled Nonlinear Schr ö dinger Equations.Using the theory of linear operators (here,2×2 matrics), we show that under a perturbation ui→ui + δui(δui= (αi(T) + ibi(T))eµδ)(i=1,2) the solitary solutions are stable. Moreover,we include the perturbation into the corresponding Hami...

Symmetry group, Hamiltonian equations and conservation laws of general three-dimensional anisotropic non-linear sourceless heat transfer equation

‎In this paper Lie point symmetries‎, ‎Hamiltonian equations and conservation‎ ‎laws of general three-dimensional anisotropic non-linear sourceless heat transfer‎ ‎equation are investigated‎. ‎First of all Lie symmetries are obtained by using the general method‎ based on invariance condition of a system of differential equations under a pro‎longed vector field‎. ‎Then the structure of symmetry ...

Stability analysis for pitchfork bifurcations of solitary waves in generalized nonlinear Schrdinger equations

Linear stability of both sign-definite (positive) and sign-indefinite solitary waves near pitchfork bifurcations is analyzed for the generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcations of linear-stability eigenvalues associated with pitchfork bifurcations are analytically calculated. Based on thes...