Solitons and Breather type solutions of some nonlinear equations by the Sine-Cosine method.

Abstract

In our recent work, we study a few nonlinear time evolution equations by the sine-cosine method and obtained a variety of generalized solitary and periodic solutions with distinct physical structures. The solutions include periodic solutions, soliton solutions, symmetric periodic soliton solutions, double periodic solutions, multiple soliton solutions, breather solutions, and kink type solutions.

Analytical solutions of fractional order Newell-Whitehead-Segel equation

“…Many significant and effective techniques have recently been created in order to discover the properties of travelling wave solutions. For instance, variational iteration [10,11], hirota bilinear transformation method [12], sub-equation method [13], backlund transform method [14], sine-cosine method [15][16][17][18], generalized tanhcoth method [19], jacobi elliptic function expansion method [20], adomianos decomposition method [21], the ( G ′ G ) method [22,23], the ( G ′ G , 1 G ) method [24], the modified ( G ′ G 2 )-expansion method [25,26] modified trial function method. [27], and so on.…”

An investigation of the physical dynamics of a traveling wave solution called a bright soliton

“…-expansion technique and the novel exponential rational function technique in 2018 [41]. Then, trigonometric soliton solutions were obtained by applying the sine-cosine method for the Zoomeron equation [42]. In 2020, exact travelling wave solutions were given using the first integral method by Zhang et al [43].…”