Travelling wave solutions and conservation laws for the Korteweg-de Vries-Bejamin-Bona-Mahony equation

Solutions and conservation laws of a generalized second extended (3+1)-dimensional Jimbo-Miwa equation

“…where ξ i , i = 1, 2, 3, 4 and η depend on x, y, z, t and u, will generate a symmetry group of (3) provided pr (4)…”

“…where pr (4) X is the fourth prolongation of X [17]. Expanding the determining equation 4and splitting on derivatives of u, we obtain an overdetermined system of linear homogeneous partial differential equations.…”

“…Nevertheless, various methods have also been established by the researchers which provide exact solutions to NLPDEs. Some of these methods are Hirota's bilinear transformation method [1], the inverse scattering method [2], Kudryashov's method [3,4], the sine-cosine method [5], the tanh-coth method [6], the simplest equation method [7,8], the tanh-function method [9], the Darboux transformation [10], the (G /G)−expansion method [11,12], the Bäcklund transformation [13], and Lie symmetry methods [14][15][16][17][18][19].…”

Optical Solitary Wave Solutions of the Space-Time Fractional Modified Equal-Width Equation and their Applications

“…In the literature, problems involving nonlinear differential equations and systems are solved by many different powerful methods, such as the extended quantum Zakharov-Kuznetsov equation by Raza, et al [10] the generalized nonlinear Klein-Gordon equation by Gepreel, et al [11] the Korteweg-de Vries-Bejamin-Bona-Mahony equation by Simbanefayi and Khalique [12] the generalized Radhakrishnan-Kundu-Lakshmanan…”

A study of a generalized first extended (3+1)-dimensional Jimbo-Miwa equation

“…Nevertheless, many methods have been developed to obtain exact solutions of the NLPDEs. These methods include the modified harmonic balance method [28], the BPVK method [31], Hirota's bilinear transformation method [21,9], the simplest equation method [16,17], the homotopy perturbation method [15], the tanh-function method [25], the Jacobi elliptic function expansion method [22], the inverse scattering method [1], the F-expansion method [38], the projective Riccati equation method [8], the tanh-coth method [33], Kudryashov's method [18,29], Lie symmetry methods [27,3,26,10,11,12,24,4,7], bifurcation method [37] and the (G /G)−expansion method [32].…”