Extracted different types of optical lumps and breathers to the new generalized stochastic potential-KdV equation via using the Cole-Hopf transformation and Hirota bilinear method

Complexiton solutions, kink soliton and breather-wave solutions for the (2+1)-dimensional combined potential Kadomtsev-Petviashvili with B-type Kadomtsev-Petviashvili equation

“…where u(x, y, t) and h 0 (x, y, t) satisfy equation (9). Therefore, according to equation (10), we can obtain some new solutions to equation (1) by solving equation (9) Case 2: When τ = 4, we get the following system:…”

“…And a large number of solutions of NLEEs with different forms such as rogue wave and lump wave solutions [4] are studied. Some methods have been proposed by scientists to study analytic solutions of NLEEs, such as Darboux transformation [5,6], the Hirota bilinear method [7][8][9][10], the inverse scattering method [11], Bäcklund transformation [12,13], exp-function method [14,15]and other methods [16][17][18].…”

Novel Analysis of Nonlinear Seventh Order Kaup-Kupershmidt Equation via the Caputo Operator

“…A variety of mathematical methods that have been created and studied [14,15,16,17,18,19] have been used to obtain the precise solution of NLFDEs. For example, the q-homotopy analysis transform approach for Navier-Stokes equations having fractional-order [20], Natural transform decomposition method for fractional modiőed Boussinesq and approximate long wave equations [24] and fractional-order kaup-kupershmidt equation [23], Yang transform decomposition method for time-fractional Fisher's equation [22] and for time-fractional Noyes-Field model [21], Elzaki homotopy perturbation technique for solving regularized long-wave equations of order fraction [25], Variational iteration transform method for fractional third order Burgers and KdV nonlinear systems [26], Modiőed Khater method for solving nonlinear fractional Ostrovsky equation [27], modiőed ( G ′ G )-expansion scheme for travelling wave solutions of fractional Boussinesq equation [28], generalized Kudryashov method for nonlinear FPDEs of Burgers type [29], Laplace residual power series approach for solving Black-Scholes Option pricing equations having fractional-order [30], őrst integral method for solving fractional Cahn-Allen equation and fractional DSW system [31] and many more [32,33,34,35,36,37,38].…”

Stability, modulation instability and traveling wave solutions of (3+1)dimensional Schrödinger model in physics

“…For the bullet solutions of such types of model many types of approaches are used, as the (3+1)dimensional Schrödinger equation can be solved by utilizing the generalized exponential rational function method (Yokus et al 2022). Many kinds of other approaches are used to study various nonlinear dynamical structures more proficiently such as the modified Jacobi elliptic expansion method Gaballah et al (2024) , the Sine-Gordon expansion method Kundu et al (2021), the Darboux transformation method (Wang et al 2021) the Khater method (Qin et al 2020), the generalized exponential rational function method (Ghanbari and Gómez-Aguilar 2019), the Riccati equation method (Akram et al 2021), the auxiliary equation method (Rezazadeh et al 2019), the unified method (Fokas and Lenells 2012), the improved F expansion technique (Islam et al 2019), the modified simple equation method (Biswas et al 2018), the exp(-( ) ) expansion technique (Lakestani and Manafian 2018), the exponential rational function method (Aksoy et al 2016), and the Hirota bilinear method (Alhami and Alquran 2022). In our study we obtain some new exact bullet solutions by using the modern techniques, also we say that according to my knowledge the methods applied in this model have not use in this model in previous, so our result are unique and newly drawn.…”