Exponentially small estimate for a generalized solitary wave solution to the perturbed K−dV equation

DOI10.1016/0362-546X(94)90093-0zbMath0811.35132OpenAlexW2009432470MaRDI QIDQ4316981

No author found.

Publication date: 19 December 1994

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(94)90093-0

zbMATH Keywords

a priori estimatesfixed point theoremintegrodifferential equationsexistence of the generalized solitary wave solution

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51)

Related Items (8)

Bifurcation of nonlinear Bloch waves from the spectrum in the Gross-Pitaevskii equation ⋮ Mass and spring dimer Fermi–Pasta–Ulam–Tsingou nanopterons with exponentially small, nonvanishing ripples ⋮ On solitary-wave solutions of fifth-order KdV type of model equations for water waves ⋮ Multi-hump solutions with small oscillations at infinity for stationary Swift–Hohenberg equation ⋮ Multi-hump solutions of some singularly-perturbed equations of KdV type ⋮ One- and two-hump solutions of a singularly perturbed cubic nonlinear Schrödinger equation ⋮ Wavelet basis analysis in perturbed periodic KdV equation ⋮ Local and global existence of solutions to initial value problems of modified nonlinear Kawahara equations

Cites Work

• Weakly non-local solitons for capillary-gravity waves: Fifth-degree Korteweg-de Vries equation
• Existence of perturbed solitary wave solutions to a model equation for water waves
• Structural stability of the Korteweg-de Vries solitons under a singular perturbation
• A theory of solitary water-waves in the presence of surface tension
• On the existence of small amplitude solitary waves with strong surface tension
• Solitary waves with surface tension. I: Trajectories homoclinic to periodic orbits in four dimensions
• On water waves at Froude number slightly higher than one and Bond number less than 1/3
• Existence of a generalized solitary wave solution for water with positive Bond number less than 1/3
• Exponentially small estimate for the amplitude of capillary ripples of a generalized solitary wave
• Solitary and periodic gravity—capillary waves of finite amplitude
• Exact solitary water waves with capillary ripples at infinity
• Water waves for small surface tension: an approach via normal form

This page was built for publication: Exponentially small estimate for a generalized solitary wave solution to the perturbed K−dV equation