An analytical–numerical method for solving the Korteweg–de Vries equation

Lattice Boltzmann method for the generalized Kuramoto–Sivashinsky equation

“…The LBM is very different from conventional numerical methods, such as the finite difference (FD) method [6,7], the heat balance integral (HBI) method [8], the finite element (FE) method [9], the spectral method [10] and the variational iteration method [11]. It is a new technique based on microscopic models and mesoscopic kinetic equations.…”

A modified tanh–coth method for solving the KdV and the KdV–Burgers’ equations

“…It has also been used to describe a number of important physical phenomena such as magnetohydrodynamics waves in a warm plasma, acoustic waves in an anharmonic crystal and ion-acoustic waves [2]. Some papers, exploring various aspects of the above, can be found in [3][4][5][6][7][8].…”

An Average Linear Difference Scheme for the Generalized Rosenau-KdV Equation

“…KdV equation has been used in very wide applications and undergone research which can be used to describe wave propagation and spread interaction as follows [1][2][3][4]:…”