Skip to main content

Generalized KdV Equation: Novel Nature Oceanic, M-lump and Physical Collision Waves Cover

.blurhash-client-img { display: none !important; }

Generalized KdV Equation: Novel Nature Oceanic, M-lump and Physical Collision Waves

Acta Mechanica et Automatica

Volume 19 (2025): Issue 2 (June 2025)

By: Hajar Farhan ISMAEL

Open Access

|Jun 2025

Figures & tables

Figures & Tables

Graphs of one-M-lump wave when z = 2, t = 2, $a_{1} = \frac{1}{5}$ , b₁ = 0.5, c₁ = 0.5, d₁ = 0.5, β = 2, γ = –1.

Plot of Eq. (12) for z = 2, $a_{1} = \frac{1}{5}$ , b₁ = 0.5, c₁ = 0.5, d₁ = 0.5, β = 2, γ = –1

Plots of 2-M-lump wave when z = 2, t = 2, a₁ = 0.5, b₁ = 0.5, $a_{2} = \frac{1}{3}$ , $b_{2} = \frac{1}{3}$ , $c_{1} = \frac{1}{3}$ , $d_{1} = \frac{1}{3}$ , $c_{2} = \frac{1}{4}$ , $d_{2} = \frac{1}{4}$ , β = 2, γ = –1.

Plots of 3-M-lump wave when z = 2, t = 2, a₁ = 0.5, b₁ = 0.5, $a_{2} = \frac{1}{3}$ , $b_{2} = \frac{1}{3}$ , $a_{3} = \frac{1}{4}$ , $b_{3} = \frac{1}{4}$ , c₁ = 0.5, d₁ = 0.5, $c_{2} = \frac{1}{5}$ , $d_{2} = \frac{1}{5}$ , $c_{3} = \frac{1}{6}$ , $d_{3} = \frac{1}{6}$ , β = 2, γ = –1

Plots of M-lump with soliton solution when z = 1, t = 2, a₁ = 0.5, b₁ = 0.5, $a_{2} = \frac{1}{3}$ , $b_{2} = \frac{1}{3}$ , k₃ = 1, l₃ = 1, j₃ = 2, λ₃ = 20, β = 2, γ = –1

Graphs of M-lump with a 2-soliton solution when z = 1, t = 2, a₁ = 0.5, b₁ = 0.5, $c_{1} = \frac{1}{3}$ , $d_{1} = \frac{1}{3}$ , k₃ = 1, l₃ = 1, j₃ = 2, λ₃ = 10, k₄ = 1, l₄ = 2, j₄ = 3, λ₄ = 20, β = 1, γ = –5

Plots of 2-M-lump with soliton solution when z = 1, t = 2, a₁ = 0.5, b₁ = 0.5, $a_{2} = \frac{1}{3}$ , $b_{2} = \frac{1}{3}$ , $c_{1} = \frac{1}{4}$ , $d_{1} = \frac{1}{4}$ , $c_{2} = \frac{1}{5}$ , $d_{2} = \frac{1}{5}$ , k₅ = 1, l₅ = 1, j₅ = 2, λ₅ = 20, β = 1, γ = –5

Graphs of complex one-soliton wave are plotted for z = 1, t = 2, k₁ = 1, l₁ = 1, j₁ = 2, α₁ = 1, β = 1, γ = 2: a) Real part, b) Imaginary part, c) Contour plot of real part, d) Contour plot of imaginary part

Graphs of complex two-soliton wave are plotted for z = 1,t = 2, k₁ = 1, k₂ = 1, l₁ = 1, l₂ = 0.5, j₁ = 0.5, j₂ = 0.5, α₁ = 3, β₂ = 1, γ₁ = 2: a) Real part, b) Imaginary part, c) Contour plot of real part, d) Contour plot of imaginary part

Graphs of complex four-soliton wave are plotted for z = 1, t = 2, k₁ = 1, k₂ = 1, k₃ = 2, l₁ = 1, l₂ = 0.5, $l_{3} = \frac{1}{3}$ , j₁ = 0.5, j₂ = 0.5, $j_{3} = \frac{1}{3}$ , α₁ = 3, α₂ = 6, α₃ = 9, β = 1, γ = 2: a) Real part, b) Imaginary part, c) Contour plot of real part, d) Contour plot of imaginary part

Graphs of complex four-soliton wave are plotted for z = 1, t = 2, k₁ = 1, k₂ = 1, k₃ = 2, k₄ = 2, l₁ = 1, l₂ = 0.5, $l_{3} = \frac{1}{3}$ , $l_{4} = \frac{1}{4}$ , j₁ = 0.5, j₂ = 0.5, $j_{3} = \frac{1}{4}$ , $j_{4} = \frac{1}{4}$ , α₁ = 3, β₂ = 6, α₃ = 9, α₄ = 12, β = 1, β = 2: a) Real part, b) Imaginary part, c) Contour plot of real part, d) Contour plot of imaginary part

Articles in this issue

DOI: https://doi.org/10.2478/ama-2025-0026 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088

Journal RSS Feed

Language: English

Page range: 217 - 223

Submitted on: Nov 30, 2024

|

Accepted on: Feb 10, 2025

|

Published on: Jun 6, 2025

Published by: Bialystok University of Technology

In partnership with: Paradigm Publishing Services

Keywords:

complex multi-soliton,

Hirota bilinear method,

long-wave method

Related subjects:

Mechanical engineering,

Bioengineering and biomedical engineering,

Civil engineering,

Environmental engineering

© 2025 Hajar Farhan ISMAEL, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2025): Issue 2 (June 2025)

Previous article