Extended homogeneous balance conditions in the sub-equation method

• Autorzy: Song Chenwei , Liu Yinping

Identyfikatory

DOI

10.1515/jaa-2021-2068

• Języki publikacji: EN

Abstrakty

EN

The sub-equation method is a kind of straightforward algebraic method to construct exact solutions of nonlinear evolution equations. In this paper, the sub-equation method is improved by proposing some extended homogeneous balance conditions. By applying them to several examples, it can be seen that new solutions could indeed be obtained.

Słowa kluczowe

EN

sub-equation method; homogeneous balance conditions; Jacobi elliptic functions; Riccati equation

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2022
• Tom: Vol. 28, nr 1
• Strony: 165--179
• Opis fizyczny: Bibliogr. 23 poz., 1 wykr.

Twórcy

autor

Song Chenwei

• Department of Computer Science and Technology, East China Normal University, Shanghai, P. R. China

autor

Liu Yinping

• School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, P. R. China

Bibliografia

• [1] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Math. Soc. Lecture Note Ser. 149, Cambridge University, Cambridge, 1991.
• [2] M. M. A. El-Sheikh, H. M. Ahmed, A. H. Arnous and W. B. Rabie, Optical solitons and other solutions in birefringent fibers with Biswas-Arshed equation by Jacobi’s elliptic function approach, Optik 202 (2020), Article ID 163546.
• [3] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000), no. 4-5, 212-218.
• [4] K. A. Gepreel, T. A. Nofal and A. A. Al-Asmari, Abundant travelling wave solutions for nonlinear Kawahara partial differential equation using extended trial equation method, Int. J. Comput. Math. 96 (2019), no. 7, 1357-1376.
• [5] K. Hosseini, M. Inc, M. Shafiee, M. Ilie, A. Shafaroody, A. Yusuf and M. Bayram, Invariant subspaces, exact solutions and stability analysis of nonlinear water wave equations, J. Ocean Eng. Sci. 5 (2020), 35-40.
• [6] X. B. Hu and H. W. Tam, New integrable differential-difference systems: Lax pairs, bilinear forms and soliton solutions, Inverse Problems 17 (2001), no. 2, 319-327.
• [7] I. A. Kunin, Elastic Media with Microstructure. I: One-Dimensional Models, Springer Ser. Solid-State Sci. 26, Springer, Berlin, 1982.
• [8] Z. B. Li and Y. P. Liu, RATH: A Maple package for finding travelling solitary wave solutions to nonlinear evolution equations, Comput. Phys. Comm. 148 (2002), no. 2, 256-266.
• [9] X. Liu and C. Liu, The relationship among the solutions of two auxiliary ordinary differential equations, Chaos Solitons Fractals 39 (2009), no. 4, 1915-1919.
• [10] Z. Y. Long, L. Y. Ping and L. Z. Bin, A connection between the (G󸀠/G)-expansion method and the truncated Painlevé expansion method and its application to the mKdV equation, Chinese Phys. B 19 (2010), no. 3, Article ID 030306.
• [11] W. X. Ma, Y. Zhang, Y. Tang and J. Tu, Hirota bilinear equations with linear subspaces of solutions, Appl. Math. Comput. 218 (2012), no. 13, 7174-7183.
• [12] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Amer. J. Phys. 60 (1992), no. 7, 650-654.
• [13] A. P. Márquez and M. S. Bruzón, Travelling wave solutions of a one-dimensional viscoelasticity model, Int. J. Comput. Math. 97 (2020), no. 1-2, 30-39.
• [14] V. B. Matveev and V. B. Matveev, Darboux Transformations and Solitons, Springer, Berlin, 1991.
• [15] A. V. Mikhailov, The reduction problem and the inverse scattering method, Phys. D 3 (1981), no. 1-2, 73-117.
• [16] R. C. Mittal and S. Pandit, Sensitivity analysis of shock wave Burgers’ equation via a novel algorithm based on scale-3 Haar wavelets, Int. J. Comput. Math. 95 (2018), no. 3, 601-625.
• [17] Y. Z. Peng, Exact solutions for some nonlinear partial differential equations, Phys. Lett. A 314 (2003), no. 5-6, 401-408.
• [18] S. Sahoo and S. Saha Ray, Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G󸀠/G)-expansion method and improved (G󸀠/G)-expansion method, Phys. A 448 (2016), 265-282.
• [19] M. Wadati, K. Konno and Y. H. Ichikawa, A generalization of inverse scattering method, J. Phys. Soc. Japan 46 (1979), no. 6, 1965-1966.
• [20] A. M. Wazwaz, The Hirota’s bilinear method and the tanh-coth method for multiple-soliton solutions of the Sawada-Kotera-Kadomtsev-Petviashvili equation, Appl. Math. Comput. 200 (2008), no. 1, 160-166.
• [21] G. Q. Xu, New types of exact solutions for the fourth-order dispersive cubic-quintic nonlinear Schrödinger equation, Appl. Math. Comput. 217 (2011), no. 12, 5967-5971.
• [22] R. X. Yao, W. Wang and T. H. Chen, New solutions of three nonlinear space- and time-fractional partial differential equations in mathematical physics, Commun. Theor. Phys. (Beijing) 62 (2014), no. 5, 689-696.
• [23] S. Zhang, New exact solutions of the KdV-Burgers-Kuramoto equation, Phys. Lett. A 358 (2006), no. 5-6, 414-420.

Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).