Conservation laws and travelling wave solutions of a generalized NLS-Boussinesq system using symmetries

Almudena P. Márquez; Tamara M. Garrido; Gaukhar Shaikhova; Rafael de la Rosa; Almudena P. Márquez; Tamara M. Garrido; Gaukhar Shaikhova; Rafael de la Rosa

doi:10.3934/era.2026348

Electronic Research Archive

2026, Volume 34, Issue 11: 8174-8202. doi: 10.3934/era.2026348

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Research article

Conservation laws and travelling wave solutions of a generalized NLS-Boussinesq system using symmetries

1.
Department of Mathematics, University of Cadiz, 11510 Puerto Real, Cadiz, Spain
2.
Department of General and Theoretical Physics, L.N. Gumilyov Eurasian National University, 010008 Astana, Kazakhstan

Received: 17 July 2026 Revised: 07 September 2026 Accepted: 15 September 2026 Published: 22 September 2026

This work investigates a coupled generalized Schrödinger-Boussinesq system with a $ p $-power nonlinearity. These equations appear in several physical applications. To begin, we present a complete classification of infinitesimal point symmetries for the system. Then, low-order local conservation laws are derived using the multiplier method, providing conserved quantities such as momentum, mass, and charge. By introducing a potential variable, we derive a Lagrangian formulation for the potential system and find nonlocal conservation laws via Noether's theorem. Finally, we explore travelling wave solutions by reducing the governing equations to a coupled autonomous system of ordinary differential equations. Several families of solutions are constructed, and their physical relevance is discussed.
- Schrödinger-Boussinesq,
- symmetries,
- conservation laws,
- Noether's theorem,
- travelling wave solutions
Citation: Almudena P. Márquez, Tamara M. Garrido, Gaukhar Shaikhova, Rafael de la Rosa. Conservation laws and travelling wave solutions of a generalized NLS-Boussinesq system using symmetries[J]. Electronic Research Archive, 2026, 34(11): 8174-8202. doi: 10.3934/era.2026348

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Abstract

This work investigates a coupled generalized Schrödinger-Boussinesq system with a $ p $-power nonlinearity. These equations appear in several physical applications. To begin, we present a complete classification of infinitesimal point symmetries for the system. Then, low-order local conservation laws are derived using the multiplier method, providing conserved quantities such as momentum, mass, and charge. By introducing a potential variable, we derive a Lagrangian formulation for the potential system and find nonlocal conservation laws via Noether's theorem. Finally, we explore travelling wave solutions by reducing the governing equations to a coupled autonomous system of ordinary differential equations. Several families of solutions are constructed, and their physical relevance is discussed.

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