<p>In this paper, we consider the deformed variant Boussinesq (DvB) system and investigate its integrability. We show that the DvB system admits a Lax pair provided the perturbation functions satisfy specific constraints. By virtue of the obtained Lax pair, we construct an infinite number of conservation laws, the Darboux transformation, and a one-soliton solution. We employ Lie symmetry analysis to compute the Lie point symmetries, similarity transformations, the associated similarity reductions, and some particular solutions of the DvB system. We also provide graphical representations of the resulting one-soliton solution and particular solutions.</p>

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INTEGRABILITY, DARBOUX TRANSFORMATION, AND SYMMETRY ANALYSIS OF DEFORMED VARIANT BOUSSINESQ SYSTEM

  • Suresh Kumar S

摘要

In this paper, we consider the deformed variant Boussinesq (DvB) system and investigate its integrability. We show that the DvB system admits a Lax pair provided the perturbation functions satisfy specific constraints. By virtue of the obtained Lax pair, we construct an infinite number of conservation laws, the Darboux transformation, and a one-soliton solution. We employ Lie symmetry analysis to compute the Lie point symmetries, similarity transformations, the associated similarity reductions, and some particular solutions of the DvB system. We also provide graphical representations of the resulting one-soliton solution and particular solutions.