Exact Solutions of the (2+1)-Dimensional Stochastic Chiral Nonlinear Schrödinger Equation

In this article, we take into account the (2+1)-dimensional stochastic Chiral nonlinear Schrodinger equation (2D-SCNLSE) in the Ito sense by multiplicative noise. We acquired trigonometric, rational and hyperbolic stochastic exact solutions, using three vital methods, namely Riccati–Bernoulli sub-ODE, He’s variational and sine–cosine methods. These solutions may be applicable in various applications in applied science. The proposed methods are direct, efficient and powerful. Moreover, we investigate the effect of multiplicative noise on the solution for 2D-SCNLSE by introducing some graphs to illustrate the behavior of the obtained solutions.

[1]  Yoshiharu Nakamura,et al.  Observation of ion acoustic multi-Peregrine solitons in multicomponent plasma with negative ions , 2017 .

[2]  E. Petrov,et al.  Exact axisymmetric solutions of the Maxwell equations in a nonlinear nondispersive medium. , 2010, Physical review letters.

[3]  W. W. Mohammed,et al.  The impact of multiplicative noise on the solution of the Chiral nonlinear Schrödinger equation , 2020, Physica Scripta.

[4]  M. Abdelrahman,et al.  The coupled nonlinear Schrödinger-type equations , 2020 .

[5]  W. Mohammed.  Approximate solution of the Kuramoto-Shivashinsky equation on an unbounded domain , 2018 .

[6]  M. Belić,et al.  Self-similar optical solitons with continuous-wave background in a quadratic–cubic non-centrosymmetric waveguide , 2019, Optics Communications.

[7]  Rashmi Srivastava,et al.  Small amplitude dust acoustic solitary wave in magnetized two ion temperature plasma , 2020, Journal of Taibah University for Science.

[8]  N. Raza,et al.  Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation , 2019 .

[9]  Elçin Yusufoglu,et al.  The variational iteration method for studying the Klein-Gordon equation , 2008, Appl. Math. Lett..

[10]  Frédéric Dias,et al.  The Peregrine soliton in nonlinear fibre optics , 2010 .

[11]  A. Wazwaz.  The integrable time-dependent sine-Gordon equation with multiple optical kink solutions , 2019, Optik.

[12]  Anjan Biswas,et al.  Phase-shift controlling of three solitons in dispersion-decreasing fibers , 2019, Nonlinear Dynamics.

[13]  N. Raza,et al.  Chiral solitons of the (1 + 2)-dimensional nonlinear Schrodinger’s equation , 2019 .

[14]  Yingying Shi,et al.  Replicator dynamics and evolutionary game of social tolerance: The role of neutral agents , 2017 .

[15]  Abdul-Majid Wazwaz,et al.  The tanh method: exact solutions of the sine-Gordon and the sinh-Gordon equations , 2005, Appl. Math. Comput..

[16]  Yan-Hai Ye,et al.  He's variational method for the Benjamin-Bona-Mahony equation and the Kawahara equation , 2009, Comput. Math. Appl..

[17]  K. Khan,et al.  The exp(-Φ(ξ))-expansion method for finding travelling wave solutions of Vakhnenko-Parkes equation , 2014 .

[18]  Mingliang Wang,et al.  The (G' G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics , 2008 .

[19]  Ji-Huan He.  A new approach to nonlinear partial differential equations , 1997 .

[20]  M. A. Sohaly,et al.  Solitary waves for the nonlinear Schrödinger problem with the probability distribution function in the stochastic input case , 2017 .

[21]  Ying Wu,et al.  Solutions of the cylindrical nonlinear Maxwell equations. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Ji-Huan He.  SOME ASYMPTOTIC METHODS FOR STRONGLY NONLINEAR EQUATIONS , 2006 .

[23]  Zhenya Yan,et al.  Abundant families of Jacobi elliptic function solutions of the (2+1)-dimensional integrable Davey–Stewartson-type equation via a new method , 2003 .

[24]  Y. Nakamura,et al.  Observation of Peregrine solitons in a multicomponent plasma with negative ions. , 2011, Physical review letters.

[25]  M. Eslami.  Soliton-like solutions for the coupled Schrodinger–Boussinesq equation , 2015 .

[26]  Abdul-Majid Wazwaz,et al.  Exact solutions to the double sinh-gordon equation by the tanh method and a variable separated ODE method , 2005 .

[27]  M. Akinlar,et al.  Soliton solutions for system of ion sound and Langmuir waves , 2020, Optical and Quantum Electronics.

[28]  H. Abdelwahed.  Nonlinearity contributions on critical MKP equation , 2020, Journal of Taibah University for Science.

[29]  Ji-Huan He,et al.  Variational principles for some nonlinear partial differential equations with variable coefficients , 2004 .

[30]  Abdul-Majid Wazwaz,et al.  A sine-cosine method for handlingnonlinear wave equations , 2004, Math. Comput. Model..

[31]  N. Hoffmann,et al.  Rogue wave observation in a water wave tank. , 2011, Physical review letters.

[32]  Hao Xiong,et al.  Kuznetsov-Ma Soliton Dynamics Based on the Mechanical Effect of Light. , 2017, Physical review letters.

[33]  Ji-Huan He.  An approximate solution technique depending on an artificial parameter: A special example , 1998 .

[34]  W. Mohammed.  Modulation Equation for the Stochastic Swift–Hohenberg Equation with Cubic and Quintic Nonlinearities on the Real Line , 2019 .

[35]  M. Wadati,et al.  Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions , 2006, nlin/0603010.

[36]  R. Hirota.  Exact solution of the Korteweg-deVries equation for multiple collision of solitons , 1971 .

[37]  M. Eslami.  Trial solution technique to chiral nonlinear Schrodinger’s equation in (1$$+$$+2)-dimensions , 2016 .

[38]  A. Abouelregal,et al.  Effects of nonlocal thermoelasticity on nanoscale beams based on couple stress theory , 2020 .

[39]  Yi Wei,et al.  A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application , 2015, Advances in Difference Equations.

[40]  Huiqun Zhang,et al.  New application of the (G ′ /G) -expansion method , 2009 .

[41]  A. Abouelregal.  A novel model of nonlocal thermoelasticity with time derivatives of higher order , 2020, Mathematical Methods in the Applied Sciences.

[42]  A. Biswas.  Conservation laws for optical solitons with anti-cubic and generalized anti-cubic nonlinearities , 2019, Optik.