The application of homotopy analysis method to solve a generalized Hirota–Satsuma coupled KdV equation

An efficient computational approach for generalized Hirota-Satsuma coupled KdV equations arising in shallow water waves

“…Now, we take the Hirota-Satsuma coupled KdV equation (18), with the following initial conditions [1,3,11,30] u(x, 0) = 1 3…”

“…Also, the soliton solution for this equation is constructed by Fan [10]. In recent years generalized Hirota-Satsuma coupled KdV equation has been analyzed by many research workers with the aid of different schemes such as Jacobi-elliptic function technique [28], the projective Riccati equations technique [29], the Adomian decomposition technique [30], the homotopy perturbation approach [11], the homotopy analysis scheme [1] and the reduced differential transform technique [3]. In recent times nonlinear differential equations have been studied by many authors by such as Baskonus et al [7], Baskonus [8,9], Rashidi et al [31][32][33] and others.…”

“…The homotopy analysis method (HAM) was initially proposed and nurtured by Liao [24][25][26][27]. This technique has been successfully applied to solve many types of nonlinear problems such as nonlinear periodic wave problems [39], Vakhnenko equation [42], Laplace equation [14], steady flow of a fourth grade fluid [36], generalized Hirota-Satsuma coupled KdV equation [2], nonNewtonian flow and heat transfer over a non-isothermal wedge [35], micropolar flow in a porous channel with mass injection [34], nonlinear fractional shock wave equation [23] etc. The Laplace transform [37] is a powerful scheme for solving various linear partial differential equations having applications in various fields such as physics, chemistry, biology and finance.…”

The Rotating Flow of Magneto Hydrodynamic Carbon Nanotubes over a Stretching Sheet with the Impact of Non-Linear Thermal Radiation and Heat Generation/Absorption

“…The Homotopy Asymptotic Method (HAM) [45][46][47][48] involves calculation expansion for velocities and the energy profile. Here, the expressions of velocities and temperature are mathematically and graphically examined.…”

Series Solution of the System of Integro-Differential Equations

“…This technique has been successfully applied to many nonlinear problems such as the viscous flows of non-Newtonian fluids [3,4], the Korteweg-de Vries-type equations [5,6], nonlinear heat transfer [7,8], finance problems [9,10], Riemann problems related to nonlinear shallow water equations [11], projectile motion [12], Glauertjet flow [13], nonlinear water waves [14], groundwater flows [15], Burgers-Huxley equation [16], time-dependent Emden-Fowler type equations [17], differential-difference equation [18], Laplace equation with Dirichlet and Neumann boundary conditions [19], thermal-hydraulic networks [20], and recently for the Fitzhugh-Nagumo equation [21], and so on. On the other hand, one of the interesting topics among researchers is solving integro-differential equations.…”