New exact solutions of sixth-order thin-film equation

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

“…Considering 𝑚 = 4 and 𝑛 = 7 in equation ( 1), we get 𝑢 𝑡 = (𝑢 4 ) 𝑥𝑥 + (𝑢 7 ) 𝑥 (10) We can get the traveling wave solutions of (1), by using the transformations 𝑢( 𝑥, 𝑡 ) = 𝑢(𝜁), 𝜁 = ( 𝑥 − 𝑐𝑡 ) (11) Substituting ( 11) into (10), we obtain the following ordinary differential equations (ODE):…”

“…For example, travailing wave variables in travelling wave solution of non-linear PDEs. numerous methods to find exact solution of nonlinear PDFs, have been suggested in the literature like: the tanh-coth method [1,2], sine-cosine method [3], homogeneous balance method [4,5], exp-function method [6], first-integral method [7], Jacobi elliptic function method [8], and (𝐺 ′ /𝐺)-Expansion method [9,10,11]. The standard method offered by Malfliet [12] is a strong technique to compute exact traveling waves solutions of non-linear partial differential equations, we will utilize the standard tanh method to find the traveling wave for a nonlinear diffusionconvection equation for different values of m and n [13,14,15].…”

New modified tanh-function method for nonlinear evolution equations

“…(10) Integrating (10) once with respect to and setting the constant of integration to zero, we obtain . ( 11) Balancing the order of with the order of in (11), we find M = 2.…”

“…And thus lead to more applications. Many powerful methods to construct exact solutions of nonlinear partial differential equations have been established and developed such as the tanh-coth method [1][2], sine-cosine method [3], homogeneous balance method [4][5], exp-function method [6], firstintegral method [7], Jacobi elliptic function method [8], and (𝐺′/𝐺)-Expansion method [9][10][11]. In this work, we will employ the modified tanhfunction method to find the exact traveling wave solutions for the Burgers-KdV equation [12] , (1) where and are arbitrary real constants with .…”

New traveling wave solutions of a nonlinear diffusion–convection equation by using standard tanh method

“…For example, travailing wave variables in travelling wave solution of non-linear PDEs. numerous methods to find exact solution of nonlinear PDFs, have been suggested in the literature like: the tanh-coth method [1,2], sine-cosine method [3], homogeneous balance method [4,5], exp-function method [6], first-integral method [7], Jacobi elliptic function method [8], and ( ′ / )-Expansion method [9,10,11]. The standard method offered by Malfliet [12] is a strong technique to compute exact traveling waves solutions of non-linear partial differential equations, we will utilize the standard tanh method to find the traveling wave for a nonlinear diffusionconvection equation for different values of m and n [13,14,15].…”