A variational characterization of 2-soliton profiles for the KdV equation
John P. Albert, Nghiem V. Nguyen
TL;DR
This paper characterizes 2-soliton solutions of the KdV equation as global minimizers of a variational problem constrained by conservation laws, providing a new variational perspective on these solutions.
Contribution
It introduces a variational characterization of 2-soliton profiles for the KdV equation using profile decomposition and conservation laws.
Findings
2-soliton solutions are global minimizers of a specific variational problem
Profile decomposition effectively characterizes multi-soliton solutions
Conservation laws play a key role in the variational formulation
Abstract
We use profile decomposition to characterize 2-soliton solutions of the KdV equation as global minimizers to a constrained variational problem involving three of the polynomial conservation laws for the KdV equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Physics Problems · Nonlinear Photonic Systems