Lie group analysis with the optimal system, generalized invariant solutions, and an enormous variety of different wave profiles for the higher-dimensional modified …

S Kumar, WX Ma, SK Dhiman, A Chauhan - The European Physical …, 2023 - Springer
In this work, the method of the Lie group of invariance is used to explore a (2+ 1)-
dimensional modified dispersive water wave (mDWW) system of equations. This system is …

Lump-type solutions and interaction phenomenon to the (2+ 1)-dimensional Breaking Soliton equation

J Manafian, B Mohammadi-Ivatloo… - Applied Mathematics and …, 2019 - Elsevier
In this article, we use the Hirota bilinear method. With the help of the symbolic calculation
and applying the used method, we solve the (2+ 1)-dimensional Breaking Soliton (BS) …

Interaction characteristics of the Riemann wave propagation in the (2+ 1)-dimensional generalized breaking soliton system

KA Muhamad, T Tanriverdi, AA Mahmud… - … Journal of Computer …, 2023 - Taylor & Francis
In this study, the nonlinear (2+ 1)-dimensional generalized breaking soliton system has
been studied by introducing an appropriate travelling wave transformation. The model under …

[HTML][HTML] Physically significant wave solutions to the Riemann wave equations and the Landau-Ginsburg-Higgs equation

HK Barman, MS Aktar, MH Uddin, MA Akbar… - Results in Physics, 2021 - Elsevier
The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH)
equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic …

Periodic type and periodic cross-kink wave solutions to the -dimensional breaking soliton equation arising in fluid dynamics

OA Ilhan, J Manafian - Modern Physics Letters B, 2019 - World Scientific
In this paper, we have acquired the periodic type and cross-kink wave solutions. In this
paper, we use the Hirota bilinear method. With the help of the symbolic calculation and …

Optical soliton solutions for the Gerdjikov–Ivanov model via tan (ϕ/2)-expansion method

J Manafian, M Lakestani - Optik, 2016 - Elsevier
In this paper, by introducing new approach, the improved tan (ϕ (ξ)/2)-expansion method
(ITEM) is further extended into Gerdjikov–Ivanov (GI) model. As a result, the hyperbolic …

Breaking theory of solitary waves for the Riemann wave equation in fluid dynamics

S Duran - International Journal of Modern Physics B, 2021 - World Scientific
In this study, analytical solutions and physical interpretations are presented for the Riemann
wave equation (RWE), which has an important physical property in fluid dynamics. The …

Analysis of Lie invariance, analytical solutions, conservation laws, and a variety of wave profiles for the (2+ 1)-dimensional Riemann wave model arising from ocean …

S Kumar, SK Dhiman, A Chauhan - The European Physical Journal Plus, 2023 - Springer
Nonlinear phenomena are common in nonlinear sciences and physical engineering, such
as ocean engineering and marine physics, as well as fluid dynamics. Nonlinear partial …

Quasiperiodic waves and asymptotic behavior for Bogoyavlenskii's breaking soliton equation in dimensions

E Fan, YC Hon - Physical Review E—Statistical, Nonlinear, and Soft …, 2008 - APS
Based on a multidimensional Riemann theta function, the Hirota bilinear method is extended
to explicitly construct multiperiodic (quasiperiodic) wave solutions for the (2+ 1)-dimensional …

[HTML][HTML] Simple equation method for nonlinear partial differential equations and its applications

TA Nofal - Journal of the Egyptian Mathematical Society, 2016 - Elsevier
In this article, we focus on the exact solution of the some nonlinear partial differential
equations (NLPDEs) such as, Kodomtsev–Petviashvili (KP) equation, the (2+ 1)-dimensional …