PT-symmetric Deformations of the Korteweg-de Vries Equation
Andreas Fring
TL;DR
This paper introduces a new class of PT-symmetric complex deformations of the Korteweg-de Vries equation, exploring their Hamiltonian structures and solitary wave solutions.
Contribution
It presents novel PT-symmetric extensions of the KdV equation, constructs associated non-Hermitian Hamiltonians, and analyzes solitary wave solutions under different boundary conditions.
Findings
Existence of conserved quantities like mass, momentum, and energy.
Construction of non-Hermitian Hamiltonians linked to the deformed equations.
Identification of solitary wave solutions for various boundary conditions.
Abstract
We propose a new family of complex PT-symmetric extensions of the Korteweg-de Vries equation. The deformed equations can be associated to a sequence of non-Hermitian Hamiltonians. The first charges related to the conservation of mass, momentum and energy are constructed. We investigate solitary wave solutions of the equation of motion for various boundary conditions.
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