Results 1 to 10 of about 1,803 (119)

Shallow-Water Wave Dynamics: Butterfly Waves, X-Waves, Multiple-Lump Waves, Rogue Waves, Stripe Soliton Interactions, Generalized Breathers, and Kuznetsov–Ma Breathers

Fractal and Fractional
A nonlinear (3+1)-dimensional nonlinear Geng equation that can be utilized to explain the dynamics of shallow-water waves in fluids is given special attention.
Sarfaraz Ahmed, Ujala Rehman, Jianbo Fei, Muhammad Irslan Khalid, Xiangsheng Chen   +4 more
doaj   +3 more sources

Computation and observation of novel interaction based on the mixed solutions to a generalized Bogoyavlensky–Konopelchenko equation

Partial Differential Equations in Applied Mathematics, 2022
A generalized Bogoyavlensky–Konopelchenko equation is introduced by using p-generalized bilinear differential operators. The lump solutions, one-lump-one-kink and one-lump-two-kink solutions are derived with symbolic computations.
Si-Jia Chen, Xing Lü, Yu-Hang Yin
doaj   +1 more source

Nonlinear superposition between lump soliton and other nonlinear localized waves for the (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Results in Physics, 2023
In the previous studies, the authors have reported the lump soliton collided with other nonlinear localized waves for (2+1)-dimensional Korteweg–de Vries–Sawada-Kotera–Ramani equation.
Longxing Li, Zhengde Dai, Bitao Cheng, Rubing Li   +3 more
doaj   +1 more source

Homoclinic breather, periodic wave, lump solution, and M-shaped rational solutions for cold bosonic atoms in a zig-zag optical lattice

Nonlinear Engineering, 2023
In this article, the equation showing the cold bosonic atoms in a zig-zag optical lattice model for some breathers, M-shaped solution and lump soliton solution, homoclinic breather pulses, breather lump pulses, periodic-cross kink wave, kink cross ...
Rizvi Syed T. R., Seadawy Aly R., Ahmed Samia   +2 more
doaj   +1 more source

Various exact wave solutions for KdV equation with time-variable coefficients

Journal of Ocean Engineering and Science, 2022
In this study, we investigate the (2 + 1)-dimensional Korteweg-De Vries (KdV) equation with the extension of time-dependent coefficients. A symbolic computational method, the simplified Hirota’s method, and a long-wave method are utilized to create ...
Hajar F. Ismael, Muhammad Amin S. Murad, Hasan Bulut   +2 more
doaj   +1 more source

Lump and Interaction solutions of a geophysical Korteweg–de Vries equation

Results in Physics, 2020
This manuscript retrieve lump soliton solution for geophysical Korteweg–de Vries equation (GKdVE) with the help of Hirota bilinear method (HBM). We will also obtain lump–kink soliton (which is interaction of lump with one kink soliton), lump-periodic ...
S.T.R. Rizvi, Aly R. Seadawy, F. Ashraf, M. Younis, H. Iqbal, Dumitru Baleanu   +5 more
doaj   +1 more source

Lump and lump-kink-type rogue-wave solutions of the homologous (3+1)-dimensional Hirota-bilinear-like equation

Results in Physics, 2023
In this article, a new dynamical system equation is constructed, named the (3+1)-dimensional Hirota-bilinear-like equation. The new ‘like’ equation has more nonlinear terms than the original equation while they have the same bilinear form.
Wenting Li, Ailing Jiao
doaj   +1 more source

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

Mathematics, 2023
This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear ...
Wen-Xiu Ma
doaj   +1 more source

Multiple lump solutions and their interactions for an integrable nonlinear dispersionless PDE in vector fields

Nonlinear Analysis, 2023
In this article, lump solutions, lump with I-kink, lump with II- kink, periodic, multiwaves, rogue waves and several other interactions such as lump interaction with II-kink, interaction between lump, lump with I-kink and periodic, interaction between ...
Tahira Batool, Aly R. Seadawy, Syed T.R. Rizvi   +2 more
doaj   +1 more source

Soliton solutions of a (2+1)-dimensional nonlinear time-fractional Bogoyavlenskii equation model

Partial Differential Equations in Applied Mathematics, 2023
In this analysis, we propose a mathematical approach named the extended (ℵ, ℜ) expansion scheme to integrate nonlinear fractional and classical evolution models. We utilize the technique to the time fractional Bogoyavlenskii equation, which signifies the
Md. Sabur Uddin, Momtaz Begum, Harun-Or-Roshid, Mohammad Safi Ullah, Alrazi Abdeljabbar   +4 more
doaj   +1 more source