Darboux transformation and explicit solutions to the generalized TD equation

Jacobi Elliptic Function Solutions and Traveling Wave Solutions of the (2 + 1)‐Dimensional Gardner‐KP Equation

“…Many well‐known models have been developed to describe the dynamics of nonlinear waves that have emerged in the recent area of modern science and engineering, such as the equation Kortewegde Vries (KdV), Kortewegde Vries Burgers equation, modified Kortewegde Vries (mKdV) equation, modified Kortewegde Vries KadomtsevPetviashvili (mKdVKP) equation, Boussinesq equation, Zakharov‐Kuznetsov‐Burgers equation, modified Kortewegde Vries ZakharovKuznetsov equation, Perergrine equation, Kawahara equation, BenjaminBonaMahoney equation, Kadomtsev PetviashviliBenjaminBonaMahony (KPBBM) equation, coupled Kortewegde Vries equation, coupled Boussinesq equation, Gardner equation, a combination of KdV and mKdV equations. Some of these techniques are used by distinct authors to discover the solitary waves solution of nonlinear evolution equations, these methods include: the modified extended mapping method, tanhsech method and the extended tanhcoth method, Kudryashov method, expansion method, auxiliary equation method, inverse scattering transform method, first integral method, Jacobi elliptic function method, modified simple equation method, lumped Galerkin method, extended simple equation method, homogeneous balance method, Darboux transformation, Backland transformation and modified extended direct algebraic method . Many of these methods are problem dependent.…”

“…techniques are used by distinct authors to discover the solitary waves solution of nonlinear evolution equations, these methods include: the modified extended mapping method, 16 tanhsech method and the extended tanhcoth method, 17,18 Kudryashov method, 19 expansion method, 20,21 auxiliary equation method, 22 inverse scattering transform method, 23 first integral method, 24 Jacobi elliptic function method, 25 modified simple equation method, [26][27][28][29] lumped Galerkin method, 30 extended simple equation method, 31 homogeneous balance method, 32 Darboux transformation, 33 Backland transformation 34 and modified extended direct algebraic method. 35 Many of these methods are problem dependent.…”

Darboux transformation and explicit solutions for the Kaup-Kupershmidt equation

“…The rogue wave and breather solution of the Gerdjikov-Ivanov equation have been derived in [17]. The Darboux transformation and explicit solutions to the generalized TD equation have been investigated in [18]. In [19], the Darboux transformation to a Dirac-type equation have been studied.…”

New Exact Solutions and Modulation Instability for the Nonlinear (2+1)-Dimensional Davey-Stewartson System of Equation

“…Current studies are underway to find new techniques to extract traveling wave solution for NLPDEs. These techniques include the tanh-sech method [1], the Jacobi elliptic function method [2], the homotopy perturbation method [3], the homogeneous balance method [4], sine-cosine method [5,6], the extended Weierstrass transformation method [7][8][9][10], the expansion method [11,12], the Bcklund transformation method [13], the inverse scattering method [14], modified extended mapping method [15], Darboux transformation [16], the extended tanh-coth method [17], Hirota bilinear method [18], modified extended direct algebraic method [19], lumped Galerkin method [20], and auxiliary equation method [21]. A lot of these methods are dependent on the type of problem and may or may not be suitable for other different problems [22][23][24][25][26][27][28][29][30][31].…”