Results 11 to 20 of about 4,439 (163)

The d-bar formalism for the modified Veselov-Novikov equation on the half-plane [PDF]

Opuscula Mathematica, 2022
We study the modified Veselov-Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems.
Guenbo Hwang, Byungsoo Moon
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Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations

Mathematical and Computational Applications, 2021
The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. It is given as third-order nonlinear partial differential equation and plays a very important role in the theory of nonlinear waves.
Keltoum Bouhali, Abdelkader Moumen, Khadiga W. Tajer, Khdija O. Taha, Yousif Altayeb   +4 more
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Integration of the Negative Order Korteweg-de Vries Equation with a Special Source

Известия Иркутского государственного университета: Серия "Математика", 2023
In this paper, we consider the negative order Korteweg-de Vries equation with a self-consistent source corresponding to the eigenvalues of the corresponding spectral problem. It is shown that the considered equation can be integrated by the method of the
G.U. Urazboev, M. M. Khasanov, I.I. Baltaeva   +2 more
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Analytical solutions of nonlinear time fractional evaluation equations via unified method with different derivatives and their comparison

Results in Physics, 2021
This paper is devoted to addressings the fairly interesting soliton solutions for the time fractional combined Korteweg-de Vries-modified Korteweg-de Vries equation (KdV–mKdV equation) and modified Burgers-KdV equation.
Muhammad Naveed Rafiq, Abdul Majeed, Shao-Wen Yao, Mohsin Kamran, Muhammad Hamza Rafiq, Mustafa Inc   +5 more
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Bistable Bright-Dark solitary wave solutions of the (3 + 1)-dimensional Breaking soliton, Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations and their applications

Results in Physics, 2017
The Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations describe weakly dispersive and small amplitude waves propagating in a quasi three-dimensional media.
Kalim Ul-Haq Tariq, A.R. Seadawy
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Fractional System of Korteweg-De Vries Equations via Elzaki Transform

Mathematics, 2021
In this article, a hybrid technique, called the Iteration transform method, has been implemented to solve the fractional-order coupled Korteweg-de Vries (KdV) equation. In this method, the Elzaki transform and New Iteration method are combined.
Wenfeng He, Nana Chen, Ioannis Dassios, Nehad Ali Shah, Jae Dong Chung   +4 more
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Solving nonlinear PDEs using the higher order Haar wavelet method on nonuniform and adaptive grids

Mathematical Modelling and Analysis, 2021
The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon ...
Mart Ratas, Andrus Salupere, Jüri Majak
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Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives

AIMS Mathematics, 2022
The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Korteweg-de Vries system is obtained in this study by employing a natural decomposition method in association with the newly established Atangana-Baleanu derivative ...
M. Mossa Al-Sawalha , Rasool Shah, Adnan Khan, Osama Y. Ababneh, Thongchai Botmart   +4 more
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Traveling wave solutions of the generalized scale-invariant analog of the KdV equation by tanh–coth method

Nonlinear Engineering, 2023
In this work, the generalized scale-invariant analog of the Korteweg–de Vries equation is studied. For the first time, the tanh–coth methodology is used to find traveling wave solutions for this nonlinear equation.
González-Gaxiola Oswaldo, Ruiz de Chávez Juan   +1 more
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On Integration of the Loaded mKdV Equation in the Class of Rapidly Decreasing Functions

Известия Иркутского государственного университета: Серия "Математика", 2021
The paper is devoted to the integration of the loaded modified Kortewegde Vries equation in the class of rapidly decreasing functions. It is well known that loaded differential equations in the literature are usually called equations containing in the ...
A.B. Khasanov, U. A. Hoitmetov
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