(2 + 1)-dimensional Boiti–Leon–Pempinelli equation – Domain walls, invariance properties and conservation laws

Symmetry and Painlevé analysis for the extended Sakovich equation

“…To get Lie symmetries of equation ( 4), we consider the standard Lie group method (Olver, 1986;Wang and Kara, 2019;Wang et al, 2020aWang et al, , 2020b. Acting by the third prolongation of the vector field or infinitesimal operator:…”

Numerical treatment of Kuramoto-Sivashinsky equation on B-spline collocation

“…The present work is related with the construction and implementation of a numerical technique to obtain the approximate solution of Kuramoto-Sivanshinsky equation (KSE) with initial-boundary conditions. The KSE is a great fundamental interest in the same way just as it is famous counterp-arts Korteweg-de Vries-Burger-Kuromato equation (Alimirzaluo & Nadjafikhah, 2019), fractional optical solitons of the space-time fractional nonlinear Schr€ odinger equations (Wu, Yu, & Wang, 2020), nonlinear wave-like equations stated by Kumar, Singh, Purohit, and Swroop (2019), symmetry breaking of infinite-dimensional dynamic system (Hu, Wang, Zhao, & Deng, 2020), vibration and elastic wave propagation in spatial flexible damping panel attached to four special spring (Hu, Zhang, & Deng, 2020), internal resonance of a flexible beam in a spatial tethered system (Hu, Ye, & Deng, 2020), minimum control energy of spatial beam with assumed attitude adjustment target (Hu, Yu, & Deng, 2020), symplectic analysis on orbit-attitude coupling dynamic problem of spatial rigid rod (Hu, Yin, Zheng, & Deng, 2020), interaction effects of DNA, RNA-polymerase, and cellular fluid on the local dynamic behaviours of DNA , different order of ordinary differential equations (Gebremedhin & Jena, 2019, 2020Jena, Mohanty, & Mishra, 2018;Mohanty, Jena, & Mishra, 2020;, B-spline collocation (Jena & Gebremedhin, 2021;Jena, Senapati, & Gebremedhin, 2020a, 2020b) symmetry analysis and rogue wave solutions for the (2 þ 1)dimensional nonlinear Schr€ odinger equation with variable coefficients (Wang, 2016), novel (3 þ 1)dimensional sine-Gorden and sinh-Gorden equation: Derivation symmetries and conservation laws (Wang, 2021), (2 þ 1)-dimensional KdV equation and mKdV equation: symmetries, group invariant solutions and conservation laws (Wang & Kara, 2019), symmetry analysis for a seventh-order generalized KdV equation and its fractional version in fluid mechanics (Wang, Liu, Wu, & Su, 2020), (2 þ 1)-dimensional Boiti-Leon-Pempinelli equation-Domail walls, invariance properties and conservation laws (Wang, Vega-Guzman, Biswas, Kamis Alzahrani, & Kara, 2020), (2 þ 1)-dimensional sine-Gordon and sinh-Gordon equations with symmetries and kink wave solution (Wang, Yang, Gu, Gua...…”

Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of Variable-Coefficients Boiti-Leon-Pempinelli Equation

“…where aðtÞ, bðtÞ, cðtÞ, dðtÞ, and eðtÞ are any functions with respect to time t. It represents the development of the components in the horizontal velocity in the x and y directions when the water wave propagates in a channel of unchanging depth and infinitely small width [9]. The vcBLP is conditionally integrable, and the necessary conditions for it to be Painlevé integrable are d ′ ðtÞeðtÞ = dðtÞe ′ ðtÞ and a ′ ðtÞbðtÞ = aðtÞb ′ ðtÞ.…”

“…Some exact solutions of vcBLP were obtained in [10] by extended tanh-function method. We can find some periodic solutions and soliton solutions of vcBLP obtained with the homogeneous balance method in [11], and the conservation laws for the constant coefficients BLP were discussed in [9]. By reviewing the relevant literatures, no one has studied vcBLP using the Lie group method.…”