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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.02601 |
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| _version_ | 1866929234209931264 |
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| author | de la Rosa, Rafael Gandarias, María Luz Bruzón, María de los Santos |
| author_facet | de la Rosa, Rafael Gandarias, María Luz Bruzón, María de los Santos |
| contents | In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva, Kuriksha and Sophocleous (2015). Equivalence group of the class under consideration has been constructed which permit an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations, based on differential substitutions, and by using the direct method of the multipliers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02601 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation de la Rosa, Rafael Gandarias, María Luz Bruzón, María de los Santos Analysis of PDEs In this paper we study the generalized variable-coefficient Gardner equations of the form $u_t + A(t)u^n\,u_x+ C(t)\,u^{2n}u_x + B(t)\,u_{xxx} + Q(t)\,u =0$. This class broadens out many other equations previously considered: Johnpillai and Khalique (2010), Molati and Ramollo (2012) and Vaneeva, Kuriksha and Sophocleous (2015). Equivalence group of the class under consideration has been constructed which permit an exhaustive study and a simple and clear formulation of the results. Some conservation laws are derived for the nonlinearly self-adjoint equations, based on differential substitutions, and by using the direct method of the multipliers. |
| title | Equivalence transformations and conservation laws for a generalized variable-coefficient Gardner equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.02601 |