Inverse scattering method for nonlinear negative first order coupled Klein-Gordon equation
Abstract
The exact N-soliton solutions are derived for the coupled negative first order Klein-Gordon (CNKG) equation subject to vanishing boundary conditions by using the inverse scattering method via Gelfand-Levitan-Marchenko equation. Based on the zero-curvature representation, the conservation laws, integrals of motion, and Hamiltonian structure of the aforementioned coupled nonlinear equations are constructed. The Jost functions and their analyticity properties for the Manakov spectral problem are recalled. The integral equations for the eigenfunctions are then used to formulate the Gel'fand-Levitan-Marchenko equations. Solving these equations establishes a direct correspondence between the kernel functions and the potential, yielding the general N-soliton expressions.
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BibTeX
@misc{sabaz2026inverse,
title = {{Inverse scattering method for nonlinear negative first order coupled Klein-Gordon equation}},
author = {Cihan Sabaz and Ilmar Gahramanov and Mansur I. Ismailov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02844},
eprint = {2609.02844},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02844},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Inverse scattering method for nonlinear negative first order coupled Klein-Gordon equation
AU - Cihan Sabaz
AU - Ilmar Gahramanov
AU - Mansur I. Ismailov
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02844
UR - https://arxiv.org/abs/2609.02844
AB - The exact N-soliton solutions are derived for the coupled negative first order Klein-Gordon (CNKG) equation subject to vanishing boundary conditions by using the inverse scattering method via Gelfand-Levitan-Marchenko equation. Based on the zero-curvature representation, the conservation laws, integrals of motion, and Hamiltonian structure of the aforementioned coupled nonlinear equations are constructed. The Jost functions and their analyticity properties for the Manakov spectral problem are recalled. The integral equations for the eigenfunctions are then used to formulate the Gel'fand-Levitan-Marchenko equations. Solving these equations establishes a direct correspondence between the kernel functions and the potential, yielding the general N-soliton expressions.
ER -