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<p>This research is carried out exploiting the similarity transformations method (STM) to solve coupled Burgers equations (CBEs). Since we have attained a new set of analytical solutions that are different from those reported before (Bai, C.L.: The exact solution of the Burgers equation and higher order Burgers equation in (2+1)-dimensions. Chinese Phys. <b>10</b>, 1091–1095 (2001), Peng, Y., Yomba, E.: New applications of the singular manifold method to the (2+1)-dimensional Burgers equations. Appl. Math. Comput. <b>150</b>, 61–67 (2006), Wazwaz, A.M.: A study on the (2+1)-dimensional and the (2+1)-dimensional higher-order Burgers equations. Appl. Math. Lett. <b>25</b>, 1495–1499 (2012)), all the solutions thus obtained for CBEs are original. The CBEs are used in various fields to represent fluids that have changing densities, especially in fluid mechanics, shock waves, gas behavior, heat transfer, sound transmission, plasma science, and traffic flows, where nonlinear effects play a significant role. The analytical solutions are followed by symmetry reductions under one-parameter Lie group transformations. The adjoint equations and conserved quantities under Lagrangian formulation are presented to prove integrability. The solutions reflect different types of wave patterns, including doubly soliton, periodic, multisoliton on a periodic surface, and soliton interactions. The inclusion of arbitrary functions and constants gives worthiness and future scope to these solutions. These solutions are critical and may involve research into plasma physics, fiber optics, fluid dynamics, biological systems, material science, and quantum field theory.</p>

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Invariant Solutions and Dynamics of Soliton to Coupled Burgers Equations

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Dig Vijay Tanwar,
  • Raj Kumar,
  • Nidhi Asthana

摘要

This research is carried out exploiting the similarity transformations method (STM) to solve coupled Burgers equations (CBEs). Since we have attained a new set of analytical solutions that are different from those reported before (Bai, C.L.: The exact solution of the Burgers equation and higher order Burgers equation in (2+1)-dimensions. Chinese Phys. 10, 1091–1095 (2001), Peng, Y., Yomba, E.: New applications of the singular manifold method to the (2+1)-dimensional Burgers equations. Appl. Math. Comput. 150, 61–67 (2006), Wazwaz, A.M.: A study on the (2+1)-dimensional and the (2+1)-dimensional higher-order Burgers equations. Appl. Math. Lett. 25, 1495–1499 (2012)), all the solutions thus obtained for CBEs are original. The CBEs are used in various fields to represent fluids that have changing densities, especially in fluid mechanics, shock waves, gas behavior, heat transfer, sound transmission, plasma science, and traffic flows, where nonlinear effects play a significant role. The analytical solutions are followed by symmetry reductions under one-parameter Lie group transformations. The adjoint equations and conserved quantities under Lagrangian formulation are presented to prove integrability. The solutions reflect different types of wave patterns, including doubly soliton, periodic, multisoliton on a periodic surface, and soliton interactions. The inclusion of arbitrary functions and constants gives worthiness and future scope to these solutions. These solutions are critical and may involve research into plasma physics, fiber optics, fluid dynamics, biological systems, material science, and quantum field theory.