Cauchy problem for the Korteweg-de Vries equation and its generalizations
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Publication:923264
DOI10.1007/BF01097030zbMath0711.35124MaRDI QIDQ923264
Publication date: 1990
Published in: Journal of Soviet Mathematics (Search for Journal in Brave)
surveygeneralized solutionsexistenceuniquenessCauchy problemcontinuous dependence on initial dataKorteweg-de Vries equationintrinsic regularitynonlocal results
KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for nonlinear higher-order PDEs (35G25)
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Weak multi-phase asymptotics for nonintegrable equations, On the Cauchy problem for the generalized Kawahara equation, An initial-boundary value problem for three-dimensional Zakharov-Kuznetsov equation, Asymptotic soliton-like solutions to the singularly perturbed Benjamin-Bona-Mahony equation with variable coefficients, Cauchy problem for the Korteweg-de Vries equation in the case of a nonsmooth unbounded initial function, On the initial-value problem for the Kawahara equation, Interaction of solitons and the effect of radiation for the generalized KdV equation
Cites Work
- On the Korteweg-de Vries equation
- Cauchy problem for modified Korteweg-de Vries equation with piecewise- type initial data
- Uniqueness of the solution of the Cauchy problem for the Korteweg-de Vries equation in classes of increasing functions
- Sur quelques généralisations de l'équation de Korteweg-de Vries
- Weighted Sobolev spaces and rapidly decreasing solutions of some nonlinear dispersive wave equations
- Solutions of the Korteweg-de Vries equation from irregular data
- The initial-value problem for the Korteweg-de Vries equation
- Method for Solving the Korteweg-deVries Equation
- Integrals of nonlinear equations of evolution and solitary waves
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