Dispersive optical solitons with Schrödinger–Hirota model having multiplicative white noise via Itô Calculus

Solitons and other nonlinear waves for stochastic Schrödinger‐Hirota model using improved modified extended tanh‐function approach

“…Overall, this study highlights the power and versatility of the improved modified extended tanh-function approach in solving stochastic nonlinear wave problems, and its potential impact on various areas of science and technology. This paper showed that the solutions obtained by this effective method are correct and new compared to the solutions obtained in [37]. Moreover, for the physical illustration of the obtained solutions, the movements of some achieved solutions were described graphically (Figures 1-20).…”

“…The focus of our current investigation is on a stochastic Schrödinger-Hirota equation with nonlinearity, which is subject to multiplicative noise in the Itô sense. This equation has been previously described in [37]:…”

“…The focus of our current investigation is on a stochastic Schrödinger‐Hirota equation with nonlinearity, which is subject to multiplicative noise in the Itô sense. This equation has been previously described in [37]: $$$$ i{\Re}_t+\hslash {\Re}_{xx}+\aleph {\left|\Re \right|}^{2n}\Re + i\gamma \left({\Re}_{xx x}+\delta {\left|\Re \right|}^{2n}{\Re}_x\right)+\sigma \mathit{\Re}\frac{dW(t)}{dt}=i\left(\tau {\Re}_x+\lambda {\left({\left|\Re \right|}^{2n}\Re \right)}_x+\kappa {\left({\left|\Re \right|}^{2n}\right)}_x\Re \right), $$$$ where $$$ \Re \left(x,t\right) $$$ is the complex function that stands for the wave profile. Also $$$ \hslash, \aleph, \gamma, \delta, \sigma, \tau, \lambda $$$, and $$$ \kappa $$$ are real valued constants.…”

Solitary wave solutions of the (4+1)-dimensional Fokas equation via an efficient integration technique

“…have been developed for both numerical and symbolic programming and thus great progress has been made in solving many non-linear problems waiting to be solved before. Many researchers started to work in this field and developed new equations (for example, Kadomtsev Petviasvili (KP) and its variants, Kdv forms, Boussinessq forms, Maccari systems, Kawahara [11][12][13][14][15][16][17][18][19][20]. The equations listed above reflect only a fraction of the equations developed in this field and studied by many researchers.…”

Optical soliton solutions of dispersive Schrödinger-Hirota equation with chromatic and inter-modal dispersion in a couple of law medium

“…where i = √ −1, u = u(x, t) is soliton profile, a, c, α are the coefficients of GVD, 3OD, IMD, respectively and b, d are the coefficients of nonlinear dispersion. Some studies about obtaining soliton solutions of the dispersive SH model can be listed as via ansatz method [6], trial equation method [14], enhanced modified extended tanh method [15], extended auxiliary equation method [16], φ 6 -expansion method [17], Hirota bilinear method [18], Adomian decomposition method [19].…”