2013 · 56 citations · 23 references
Natural SciencesMathematicsPhysicsDifferential EquationsFluid DynamicsInitial Value ProblemsNumerical AlgorithmsNumerical AnalysisNumerical ConvergenceNumerical Methods For Differential EquationsPartial Differential EquationsKorteweg - De Vries EquationNumerical Methods For Initial Value ProblemsSteepest DescentTime-stepping Schemes
Abstract. We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation with steplike initial data. 1.
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Percy Deift, T. Kriecherbauer, K. T-R McLaughlin et al. · Communications on Pure and Applied Mathematics · 1999 · 850 citations
Theta functions and non-linear equations
Boris Dubrovin · Russian Mathematical Surveys · 1981 · 671 citations