Volume 66 | Issue 3 | Year 2020 | Article Id. IJMTT-V66I3P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I3P512
This study examines the new different varieties of soliton structures of the unstable nonlinear Schrodinger equation through the generalized Kudryshov method. This model has valuable applications in mathematical physics. The obtained new different types of soliton structures are represented in names of the rational, and exponential functions show that the considered approach is useful to investigate the nonlinear dispersive equations in mathematical physics.
[1] M. N. Alam and C. Tunc, Constructions of the optical solitons and other solitons to the conformable fractional ZakharovKuznetsov equation with power law nonlinearity, Journal of Taibah University for Science, 14 (1), 94-100, 2020.
[2] M. N. Alam and X. Li, New soliton solutions to the nonlinear complex fractional Schro¨dinger equation and the conformable time-fractional Klein-Gordon equation with quadratic and cubic nonlinearity, Physica Scripta, 95 (4), 045224, 2020.
[3] M. N. Alam and C. Tunc, The new solitary wave structures for the (2 + 1)-dimensional timefractional Schrodinger equation and the space-time nonlinear conformable fractional Bogoyavlenskii equations, Alexandria Engineering Journal, Available online 21 February 2020, DOI: https://doi.org/10.1016/j.aej.2020.01.054.
[4] M. N. Alam, Exact solutions to the foam drainage equation by using the new generalized (G ′/G )- expansion method, Results in Physics 5 , 168-177, 2015.
[5] M. N. Alam and X. Li, Exact traveling wave solutions to higher order nonlinear equations, Journal of Ocean Engineering and Science, 4(3), 276-288, 2019.
[6] M. N. Alam, M. A. Akbar and S. T. Mohyud-Din, A novel (G ′/G )-expansion method and its application to the Boussinesq equation, Chin. Phys. B, 23(2), 020203, 2014.
[7] M.N. Alam and M. M. Alam, An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules, Journal of Taibah University for Science, 11, 939-948, 2017.
[8] M. N. Alam and C. Tunc, An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator-prey system, Alexandria Engineering Journal, 55, 1855-1865, 2016.
[9] V. S. Kumar, H. Rezazadeh, M. Eslami, F. Izadi and M. S Osman, Jacobi Elliptic Function Expansion Method for Solving KdVEquation with Conformable Derivative and Dual-Power LawN onlinearity, Int. J. Appl. Comput. Math 5, 127, 2019..
[10] A. A. Omar, Application of residual power series method for the solution of time-fractional Schrodinger equations in one-dimensional space, Fundamenta Informaticae 166, 87-110, 2019.
[11] W. Sikander, U. Khan, N. Ahmed and S. T. Mohyud-Din, Optimal solutions for homogeneous and non-homogeneous equations arising in physics, Results in Physics, 7, 216-224, 2017.
[12]M. Mirzazadeh, R.T. Alqahtani and A. Biswas, Optical soliton perturbation with quadratic-cubic nonlinearity by Riccati-Bernoulli sub-ODE method and Kudryashov’s scheme, Optik, 145, 74, 2017.
[13]A. R. Seadawy and S. Z. Alamri, Mathematical methods via the nonlinear two-dimensional water waves of Olver dynamical equation and its exact solitary wave solutions, Results Phys, 8, 286, 2018.
[14]A. R. Seadawy, Ion acoustic solitary wave solutions of two-dimensional nonlinear KadomtsevPetviashviliBurgers equation in quantum plasma, Math. Meth. Appl. Sci., 40, 15981607, 2017.
[15]A. R. Seadawy, Three-Dimensional Weakly Nonlinear Shallow Water Waves Regime and its Traveling Wave Solutions, International Journal of Computational Methods, 15 (3), 1850017, 2018.
[16]A. R. Seadawy, Solitary wave solutions of two-dimensional nonlinear KadomtsevPetviashvili dynamic equation in dust-acoustic plasmas, Pramana-J. Phys, 89, 49, 7, 2017.
[17]A. R. Seadawy, Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods, Eur Phys J Plus, 132, 518, 2017.
[18]M. S. Osman, One-soliton shaping and inelastic collision between double solitons in the fifth-order variable-coefficient SawadaKotera equation, Nonlinear Dynamics, 96 (2), 14911496, 2019.
[19]M. S. Osman, B. Ghanbari and J. A. T. Machado, New complex waves in nonlinear optics based on the complex Ginzburg-Landau equation with Kerr law nonlinearity, The European Physical Journal Plus, 134, 20, 2019.
[20]M. S. Osman and A. M. Wazwaz, A general bilinear form to generate different wave structures of solitons for a (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation, Math Meth Appl Sci. 17, 2019, DOI: 10.1002/mma.5721.
[21]K. Hosseini, D. Kumar, M. Kaplan and E. Y. Bejarbaneh, New exact traveling wave solutions of the unstable nonlinear Schrodinger equations, Commun. Theor. Phys., 68, 761767, 2017.
[22]D. Lu, A. R. Seadawy and A. Ali, Structure of traveling wave solutions for some nonlinear models via modified mathematical method , Open Phys., 16: 854860, 2018.
[23]A. A. Gaber, A. F. Aljohani, A. Ebaid and J. T. Machado, The generalized Kudryashov method for nonlinear spacetime fractional partial differential equations of Burgers type, Nonlinear Dynamics, 95, 361368, 2019.
Md. Azizur Rahman, Md. Nur Alam, "The generalized Kudryshov method applied to the unstable nonlinear Schrodinger equation in mathematical physics," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 3, pp. 82-89, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I3P512