Different analytical approaches for finding novel optical solitons with generalized third-order nonlinear Schrödinger equation

New soliton solutions of kraenkel-manna-merle system with beta time derivative

“…Thus, exponential function solution, complex exponential function solution, complex hyperbolic function solution and complex dark soliton solutions of the considered equation are obtained. In this The most important advantage of the method used in this study is that a wide variety of solution families can be created for each different value of p i and q i , (i = 1, 4) in equation (7). since it offers a wide range of solution families, it is a more general method than other methods.…”

“…equality is achieved. So the obtained different states of the considered equation via GERFM are as follows: Family 1: For p = [ − 2, − 1, 1, 1] and q = [0, 1, 0, 1], equation (7) turns into the form,…”

“…Nonlinear evolution equations (NLEEs) have important applications in mathematical chemistry, mathematical physics, hydrodynamics, biophysics, geochemistry, control theory, mechanics, meteorology, chemical kinematics, optics, biogenetics and many other fields of science. Many researchers have presented various solution methods to obtain the solutions of NLEEs [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Soliton: A dispersion-less solution with existence and its types

“…It is also helpful in problem of optical pulse propagation in asymmetric, twin core optical fibers etc. Optical solitons, which are one of the most important solutions of nonlinear Schrodinger equation, are used in optical fiber communication [ 44 , 48 , 64 , 65 , 66 , 67 , 68 , 69 ].…”

A study on the solutions of (1+1)-dimensional Mikhailov-Novikov-Wang equation

“…NLEEs have very important applications in areas such as mathematical physics, optical fibers, mathematical chemistry, hydrodynamics, fluid dynamics, geochemistry, control theory, meteorology, optics, mechanics, chemical kinematics, biophysics, biogenetics, and so on. A number of methods have been developed by various researchers in order to obtain solutions of NLEEs, which have such important areas of use in the scientific world: Modified direct algebraic, modified Kudryashov and trigonometric-quantic B-spline methods [1], improved Bernoulli sub-equation function method [2], modified extended tanh-function method [3], new extended generalized Kudryashov and generalized new Kudryashov methods [4], new function method [5], exp -φ(ξ) method [6], double (G /G, 1/G)-expansion method [7], modified extended tanh-expansion based method [8], modified simple equation method [9], Jacobi elliptic function expansion method [10], modified (1/G )-expansion method [11]. (1+1)-dimensional MNWIE is given as [12]:…”