Exploration of Higher-order Nondegenerate Soliton solutions for Manakov model via Gram-determinant Darboux transformation

K N Santhiya; P S Vinayagam

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arXiv · 2606.24920

Exploration of Higher-order Nondegenerate Soliton solutions for Manakov model via Gram-determinant Darboux transformation

K N Santhiya·P S Vinayagam

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Abstract

Higher-order nondegenerate soliton solutions of the integrable Coupled Nonlinear Schrodinger system, known as the Manakov system, are obtained using the Darboux transformation associated with the Gram-determinant approach. Starting from the trivial seed solution, the explicit first and second-order soliton solutions are constructed through the direct iterative Darboux procedure. Owing to the rapid increase in algebraic complexity with successive iterations, the higher-order solutions are reformulated through a compact Gram-determinant representation, thereby establishing a unified and systematic framework for their construction. Using this approach, explicit third- and fourth-order solutions are derived, and the general Nth-order case is presented. The resulting structures exhibit asymmetric localized profiles with multiple intensity peaks arising from distinct spectral parameters. The collision dynamics of higher-order nondegenerate solitons reveal features such as asymmetric energy redistribution and complex interaction behaviour. The present formulation provides a systematic and explicit construction of higher-order nondegenerate solitons, offering new insights into multi-component nonlinear wave dynamics.

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K N Santhiya, P S Vinayagam. 2026-06-20. Exploration of Higher-order Nondegenerate Soliton solutions for Manakov model via Gram-determinant Darboux transformation. https://arxiv.org/abs/2606.24920

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