Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method

Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2Sirisubtawee1, Koonprasert2 2018Advances in Mathematical Physics440210View full textAdd to dashboardCite

“…Substituting (49) into (47) and (48) and then integrating once, we know that (47) and (48) give the same equation as follows:…”

“…The analytical solution was expressed in terms of a square of the exponential secant function. Later, Sekulić et al [47] applied the modified extended tanh-function method to solve (28) for exact traveling wave solutions. The solutions were written as the square of the following functions: tan, cot, tanh, and coth.…”

“…One of the important models in such fields is the nonlinear transmission line model for nanoionic currents along microtubules (MTs) segmented into identical elementary rings (ERs). The model is playing an important role in cellular signalling and the elaborated details of derivation of the equation can be found in [46,47]. The equation of nanoionic currents along MTs is described as follows [47]:…”

“…The model is playing an important role in cellular signalling and the elaborated details of derivation of the equation can be found in [46,47]. The equation of nanoionic currents along MTs is described as follows [47]:…”

The Backlund Transformation of the Generalized Riccati Equation and Its Applications to the Nonlinear KPP Equation

“…Nonlinear wave phenomena of dispersion, dissipation, diffusion, reaction and convection are very important in nonlinear wave equations. In recent decades, many effective methods have been established to obtain exact solutions of nonlinear PDEs, such as the inverse scattering transform [1], the Hirota method [2], the truncated Painlevé expansion method [3], the Bäcklund transform method [1,4,5], the exp-function method [6][7][8], the simplest equation method [9,10], the Weierstrass elliptic function method [11], the Jacobi elliptic function method [12][13][14], the tanh-function method [15,16], the ( / G) G′ expansion method [17][18][19][20][21][22], the modified simple equation method [23][24][25][26], the Kudryashov method [27][28][29], the multiple exp-function algorithm method [30,31], the transformed rational function method [32], the Frobenius decomposition technique [33], the local fractional variation iteration method [34], the local fractional series expansion The objective of this article is to use the Bäcklund transformation of the generalized Riccati equation to construct new exact traveling wave solutions of the following nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation [22,26,46]. [22] have discussed Equation (1.1) using the ( / G) G′ -expansion method and found its ex...…”