Solitons and peakons of a nonautonomous Camassa–Holm equation

Huang, Yunzhe; Yu, Xin

doi:10.1016/j.aml.2019.06.040

Cited by 4 publications

(2 citation statements)

References 23 publications

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“…The behaviors of solutions to the CH equation with dissipative term and dispersion term are studied in [25]. The local well-posedness for the Cauchy problem of the CH type equations [6,15,20,26,[28][29][30][31], asymptotic stability [17,22], solitons solutions [14], and regularity of conservative solutions [18] are considered. The readers may refer to [8-10, 18, 20-22] Molinet [23] considers the peakon solutions of the DP equation.…”

Section: (11)mentioning

confidence: 99%

Well-posedness and behaviors of solutions to an integrable evolution equation

Ming

Lai

2020

Bound Value Probl

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This work is devoted to investigating the local well-posedness for an integrable evolution equation and behaviors of its solutions, which possess blow-up criteria and persistence property. The existence and uniqueness of analytic solutions with analytic initial values are established. The solutions are analytic for both variables, globally in space and locally in time. The effects of coefficients λ and β on the solutions are given.

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Section: (11)mentioning

confidence: 99%

Well-posedness and behaviors of solutions to an integrable evolution equation

Ming

Lai

2020

Bound Value Probl

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“…In this way, both numerical and analytical computational techniques, methods and models have been developed and successfully applied in the solution of many non-linear equations. As an example of these equations, we can give: Schrodinger equation [13], Camassa-Holm equation [15], Kundu-Muhherjee-Naskar model [16], Biswas-Milovic equation [17], Triki-Biswas equation [18], Radhakrishnan-Kundu-Lakshmanan model [19], Kdv forms [20], Zoomeron equation [21], Fornberg-Whitham equation [22], Mikhailov-Novikov-Wang equation [23], Kawahara equation [24], Biswas-Arshed equation [25] and many more. One of these equations is nonlinear reaction-diffusion equation which has a large application area.…”

Section: Introductionmentioning

confidence: 99%

Soliton solutions of (2+1)-dimensional non-linear reaction-diffusion model via Riccati-Bernoulli approach

Albayrak

2022

THERM SCI

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In this study, soliton solutions of the (2+1)-dimensional reaction-diffusion equation are investigated by the extended Kudryashov method based on Riccati-Bernoulli approach. Firstly, we obtained the non-linear ordinary differential form of the (2+1)-dimensional non-linear reaction-diffusion equation by implementing the wave transformation. Then, the extended Kudryashov method has been presented and applied to the non-linear ordinary differential form. By applying the extended Kudryashov method the polynomial form has been gained, solution sets have been obtained and soliton solutions have been formed by taking the appropriate sets. Finally, some graphical representations of the gained results for instance bright, dark, kink and singular solutions are presented and commented. Within the scope of the article, the study on investigating the soliton solutions of the (2+1)-dimensional non-linear reaction-diffusion equation via the extended Kudryashov approach has not been studied and the obtained results have not been reported.

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