New soliton configurations for two different models related to the nonlinear Schrödinger equation through a graded-index waveguide
Source abstract
Abstract
The present paper studies two various models with two different types: the nonlinear Schrödinger equation with power-law nonlinearity and the (3 + 1)-dimensional nonlinear Schrödinger equation. We perform the modified (G′G)-expansion method to find some exact solutions and to construct various types of solitary wave phenomena for each equation. The received aspects contribute to the firm mathematical foundation and might be essential to the soliton waves. As a result, we obtain all the solutions from Wazwaz [Math. Comput. Modell. 43, 178–184 (2016)] and also obtain some new soliton solutions.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Nonlinear Waves and Solitons · Nonlinear Photonic Systems · Advanced Fiber Laser Technologies
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Department of Mathematics, College of Sciences, Jazan University 1 , Jazan 45142, Saudi Arabia
Department of Mathematics, Pabna University of Science and Technology 2 , Pabna 6600, Bangladesh
Department of Mathematics, Bangladesh University of Engineering and Technology 3 , Dhaka-1000, Bangladesh
Department of Mathematics, Faculty of Science, Cairo University 4 , Giza 12316, Egypt
References (52)
Show source-provided references
1. Multi-soliton rational solutions for quantum Zakharov-Kuznetsov equation in quantum magnetoplasmas10.1080/17455030.2016.1166288 ↗
2. Double-wave solutions and lie symmetry analysis to the (2 + 1)-dimensional coupled Burgers equations10.1016/j.cjph.2019.11.005 ↗
3. Equilibrium investigation of complex formation reactions involving copper(II), nitrilo-tris(methyl phosphonic acid) and amino acids, peptides or DNA constitutents. The kinetics, mechanism and correlation of rates with complex stability for metal ion promoted hydrolysis of glycine methyl ester10.1080/00958970600561399 ↗
4. Synthesis, characterization and molecular modeling of new ruthenium(II) complexes with nitrogen and nitrogen/oxygen donor ligands10.1016/j.arabjc.2015.04.001 ↗
5. Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model10.1016/j.chaos.2020.110089 ↗
6. Abundant complex wave solutions for the nonautonomous Fokas–Lenells equation in presence of perturbation terms10.1016/j.ijleo.2018.12.064 ↗
7. Solitary wave solution of the two-dimensional regularized long wave and Davey-Stewartson equations in fluids and plasmas10.4236/am.2012.38124 ↗
8. Gausson parameter dynamics in ENZ-material based waveguides using moment method10.1016/j.ijleo.2020.165273 ↗
9. Optical solitons with Sasa–Satsuma equation by Laplace–Adomian decomposition algorithm10.1016/j.ijleo.2021.166262 ↗
10. Pure-cubic optical soliton perturbation with full nonlinearity by unified Riccati equation expansion10.1016/j.ijleo.2020.165445 ↗
11. Nonlinear Schrodinger equations with spatio-temporal dispersion in Kerr, parabolic, power and dual power law media: A novel extended Kudryashov’s algorithm and soliton solutions10.1016/j.rinp.2017.08.008 ↗
12. A sine-cosine method for handling nonlinear wave equations10.1016/j.mcm.2003.12.010 ↗
13. Closed form solutions for nonlinear biological population model10.1142/s0218339018500109 ↗
14. Modified extended exp-function method for system of nonlinear partial differential equations defined by seismic sea waves10.1007/s12043-018-1601-6 ↗
15. Jacobi elliptic function solutions for two variant Boussinesq equations10.1016/j.chaos.2004.09.085 ↗
16. On the new soliton and optical wave structures to some nonlinear evolution equations10.1140/epjp/i2017-11738-7 ↗
17. Complex acoustic gravity wave behaviors to some mathematical models arising in fluid dynamics and nonlinear dispersive media10.1007/s11082-017-1286-y ↗
18. New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications10.1016/j.rinp.2019.102491 ↗
19. Exact solutions for a reaction diffusion equation by using the generalized tanh method
20. Homotopy Perturbation transform method for solving ion hyperbolic partial differential equations10.1016/j.camwa.2007.10.032 ↗
21. Invariance analysis, exact solution and conservation laws of (2 + 1) dim fractional Kadomtsev-Petviashvili (KP) system10.3390/sym13030477 ↗
22. A (2 + 1)-dimensional Kadomtsev–Petviashvili equation with competing dispersion effect: Painlevé analysis, dynamical behavior and invariant solutions10.1016/j.rinp.2021.104043 ↗
23. Microtubules nonlinear models dynamics investigations through the exp(−ϕ(ξ))-expansion method implementation10.3390/math4010006 ↗
24. An analytical method for solving exact solutions of the nonlinear Bogoyavlenskii equation and the nonlinear diffusive predator-prey system10.1016/j.aej.2016.04.024 ↗
25. An analytical method for solving exact solutions of a nonlinear evolution equation describing the dynamics of ionic currents along microtubules10.1016/j.jtusci.2016.11.004 ↗
26. Exponential prototype structure for (2 + 1)-dimensional Boiti-Leon-Pempinelli systems in mathematical physics10.1080/17455030.2015.1132860 ↗
27. The (G′/G)-expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics10.1016/j.physleta.2007.07.051 ↗
28. A novel (G′/G)-expansion method and its application to the Boussinesq equation10.1088/1674-1056/23/2/020203 ↗
29. A generalized (G′/G)-expansion method and its applications10.1016/j.physleta.2008.02.027 ↗
30. An improved (G′/G)-expansion method for solving nonlinear evolution equations10.1080/00207160802450166 ↗
31. Exact solutions to the foam drainage equation by using the new generalized (G′/G)-expansion method10.1016/j.rinp.2015.07.001 ↗
32. Exact traveling wave solutions of the (3 + 1)-dimensional mKdv-ZK equation and the (1 + 1)-dimensional compound KdVB equation using new approach of the generalized (G′/G)-expansion method10.1007/s12043-014-0776-8 ↗
33. On shallow water waves in a medium with time-dependent dispersion and nonlinearity coefficients10.1016/j.jare.2014.02.004 ↗
34. Analytical and numerical solutions of mathematical biology models: The Newell-Whitehead-Segel and Allen-Cahn equations10.1002/mma.6067 ↗
35. Analytical study of solitons to Benjamin-Bona-Mahony-Peregrine equation with power law nonlinearity by using three methods
36. Multi-soliton rational solutions for some nonlinear evolution equations10.1515/phys-2015-0056 ↗
37. Constructions of the optical solitons and other solitons to the conformable fractional Zakharov–Kuznetsov equation with power law nonlinearity10.1080/16583655.2019.1708542 ↗
38. New soliton solutions to the nonlinear complex fractional Schrodinger equation and the conformable time-fractional Klein–Gordon equation with quadratic and cubic nonlinearity10.1088/1402-4896/ab6e4e ↗
39. Reliable analysis for nonlinear Schrodinger equations with a cubic nonlinearity and power law nonlinearity10.1016/j.mcm.2005.06.013 ↗
40. Constructing of exact solutions to the nonlinear Schrodinger equation (NLSE) with power-law nonlinearity by the Weierstrass elliptic function method10.1016/j.ijleo.2015.10.213 ↗
41. Generalized method and its application in the higher order Schrodinger equation in nonlinear optical fibers10.1016/s0960-0779(02)00435-6 ↗
42. New exact complex travelling wave solutions to nonlinear Schrodinger (NLS) equation10.1016/j.cnsns.2007.11.014 ↗
43. 1995
44. 2006
45. 1981
46. 1993
47. 1980
48. Periodic solutions of the Korteweg-de Vries equation10.1002/cpa.3160280105 ↗
49. Reliable analysis for obtaining exact soliton solutions of nonlinear Schrodinger equation10.1016/j.chaos.2006.11.006 ↗
50. Exact solitary wave solutions of the complex nonlinear Schrodinger equations10.1016/j.ijleo.2016.02.008 ↗
51. New solitary wave structures to the (3 + 1)-dimensional Kadomtsev-Petviashvili andSchrdinger equation10.1016/j.joes.2019.06.002 ↗
52. 1997