Guodong Yin, Nan Chen, Pu Li
<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A <formula formulatype="inline"><tex>$\mu$</tex></formula>-synthesis robust controller of a four-wheel steering (4WS) vehicle is designed with the optimized weighting functions to attenuate the external ...
Harun-Or-Roshid, Wen‐Xiu Ma
To explore the features of lump solutions, which are local in every direction of space, a ( 2 + 1 )-dimensional extended shallow water wave model is studied, based on its bilinear representation. Several ansatzes have been utilized to determine single lump waves, lump-kink waves, single kinks and mu...
M. Mamun Miah, H. M. Shahadat Ali, M. Ali Akbar, Abdul–Majid Wazwaz
Dipankar Kumar, Choonkil Park, Nishat Tamanna, Gour Chandra Paul et al.
New dual-wave soliton solutions are addressed for the two-mode Sawada-Kotera (TmSK) equation arising in fluids by the modified Kudryashov and new auxiliary equation methods. As outcomes, bright, dark, periodic, and singular-periodic dual-wave solutions are obtained. The graphs of the solutions are p...
Harun-Or Roshid, Md. Rashed Kabir, Rajandra Chadra Bhowmik, Bimal Kumar Datta
In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential ...
Mostafa M. A. Khater, Dipankar Kumar
The aim of the article is to construct exact solutions for the time fractional coupled Boussinesq–Burger and approximate long water wave equations by using the generalized Kudryashov method. The fractional differential equation is converted into ordinary differential equations with the help of fract...
Abdulla – Al – Mamun, Tianqing An, Nur Hasan Mahmud Shahen, Samsun Nahar Ananna et al.
In this paper, the new 3D fractional Wazwaz-Benjamin-Bona-Mahony (WBBM) equations newly announced are investigated with the introduction of the spatial and sequential fractional-order derivatives expending in the sense of conformable derivative. Several solutions containing hyperbolic and trigonomet...
M. Ali Akbar, Farah Aini Abdullah, Md. Tarikul Islam, Mohammed A. Al Sharif et al.
For uni-directional wave transmission in the smooth bottom of shallow sea water and the superconductivity of nonlinear media with dispersion systems, the (1 + 1)-dimensional Camassa-Holm and Landau-Ginzburg-Higgs equations are of particular interest in research to the academics. Analytical wave solu...
M. Ali Akbar, Abdul–Majid Wazwaz, Forhad Mahmud, Dumitru Bǎleanu et al.
The perturbed nonlinear Schrödinger (NLS) equation and the nonlinear radial dislocations model in microtubules (MTs) are the underlying frameworks to simulate the dynamic features of solitons in optical fibers and the functional aspects of microtubule dynamics. The generalized Kudryashov method is u...
Purobi Rani Kundu, Md. Rezwan Ahamed Fahim, Md. Tarikul Islam, M. Ali Akbar
The Estevez-Mansfield-Clarkson (EMC) equation and the (2+1)-dimensional Riemann wave (RW) equation are important mathematical models in nonlinear science, engineering and mathematical physics which have remarkable applications in the field of plasma physics, fluid dynamics, optics, image processing ...
Md. Habibul Bashar, S. M. Rayhanul Islam
In this article, we implement the modified simple equation (MSE) and improve F-expansion method to find the exact solutions of the (2 + 1)-dimensional Heisenberg Ferromagnetic Spin Chain (HFSC) equation and construct traveling wave solutions in terms of hyperbolic functions, trigonometric function...
Xiangyong Chen, Tingwen Huang, Jinde Cao, Ju H. Park et al.
This study mainly investigates finite‐time multi‐switching synchronisation of multiple uncertain complex chaotic systems with network transmission mode. Both the unknown parameters and disturbances are considered. By establishing the desired multi‐switching rules, the definition of finite‐time hybri...
M. Ali Akbar, Norhashidah Hj. Mohd. Ali
The improved F-expansion method combined with Riccati equation is one of the most effective analytical methods in finding the exact traveling wave solutions to non-linear evolution equations in mathematical physics. In this article, this method is implemented to investigate new exact solutions to th...
Kamruzzaman Khan, M. Ali Akbar, Md. Nur Alam
In this paper, the modified simple equation (MSE) method is implemented to find the exact solutions for the nonlinear Drinfel’d–Sokolov–Wilson (DSW) equation and the modified Benjamin–Bona–Mahony (mBBM) equations. The efficiency of this method for constructing these exact solutions has been demonstr...
Hadi Rezazadeh, Dipankar Kumar, Ahmad Neirameh, Mostafa Eslami et al.