On the dynamics of optical soliton solutions, modulation stability, and various wave structures of a (2+1)-dimensional complex modified Korteweg-de-Vries equation using two integration mathematical methods

Rani, Setu; Kumar, Sachin; Mann, Nikita

doi:10.1007/s11082-023-04946-y

Cited by 38 publications

(3 citation statements)

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“…where v represents a constant velocity. After applying this transformation, Eq (11) is converted to an ODE as…”

Section: Fist Step the Following Traveling Wave Transformation Is Usedmentioning

confidence: 99%

“…Fifth step. Lastly, exact solutions of Eq (11) are obtained by plugging the values a 0 , a j , b j , where j = (1, 2, 3. . ., M) Y, δ and v along with Eqs (20)- (24) into Eq (15).…”

Section: Plos Onementioning

confidence: 99%

“…The methods of finding exact solutions of NLEEs using traveling wave transformations are a popular topic of research. Many useful methods have been employed for extracting solitary wave solutions, such as; improved tan �ðxÞ 2 À � expansion method [3], first integral method [4], modified auxiliary equation method [5], generalized exponential rational function (GERF) method [6], an inverse-G 0 G expansion method [7], the Lie classical method and unified method [8], the modified generalized Riccati equation mapping approach [9], the modified generalized exponential rational function method and the extended function method [10], new modified generalized Riccati equation mapping approach [11] and others.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of perturbed Boussinesq equation via novel integrating schemes

Vivas-Cortez,

Arshed,

Perveen

et al. 2024

PLoS ONE

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To analyze and study the behaviour of the shallow water waves, the perturbed Boussinesq equation has acquired fundamental importance. The principal objective of this paper is to manifest the exact traveling wave solution of the perturbed Boussinesq equation by two well known techniques named as, two variables ( G ′ G , 1 G ) expansion method and generalized projective Riccati equations method. A diverse array of soliton solutions, encompassing periodic, bright solitons, singular solitons and bright singular solitons are obtained by the applications of proposed techniques. The constraint conditions for newly constructed solutions are also specified. To enhance comprehension, the numerical illustrations of constructed solutions have been represented using surface plots, 2D plots and density plots. The results delineated in this paper transcend existing analysis, offering a novel, well-structured, and modern perspective. The solutions obtained not only enrich understanding of shallow water wave models but also exhibit efficacy in providing detailed descriptions of their dynamics.

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“…where v represents a constant velocity. After applying this transformation, Eq (11) is converted to an ODE as…”

Section: Fist Step the Following Traveling Wave Transformation Is Usedmentioning

confidence: 99%

“…Fifth step. Lastly, exact solutions of Eq (11) are obtained by plugging the values a 0 , a j , b j , where j = (1, 2, 3. . ., M) Y, δ and v along with Eqs (20)- (24) into Eq (15).…”

Section: Plos Onementioning

confidence: 99%