Solitary wave and shock wave solitons to the transmission line model for nano-ionic currents along microtubules

In this letter, the solitary wave and shock wave solitons for nonlinear equation of special interest in nanobiosciences, namely the transmission line model for nano-ionic currents along microtubules, have been constructed successfully. The solitary wave ansatz is used to carry out the solutions which shows the consistency.

[1]  T F Nonnenmacher,et al.  A fractional calculus approach to self-similar protein dynamics. , 1995, Biophysical journal.

[2]  Jincun Liu,et al.  Numerical solutions of the space- and time-fractional coupled Burgers equations by generalized differential transform method , 2011, Appl. Math. Comput..

[3]  M. Younis.  The First Integral Method for Time-Space Fractional Differential Equations , 2013 .

[4]  Zhaosheng Feng,et al.  An exact solution to the Korteweg-de Vries-Burgers equation , 2005, Appl. Math. Lett..

[5]  A. Bekir,et al.  Bright and dark soliton solutions for variable-coefficient diffusion–reaction and modified Korteweg–de Vries equations , 2012 .

[6]  M. Younis,et al.  The modified simple equation method for solving nonlinear Phi-Four equation , 2013 .

[7]  Min Chen,et al.  Exact solutions of various Boussinesq systems , 1998 .

[8]  Zuntao Fu,et al.  JACOBI ELLIPTIC FUNCTION EXPANSION METHOD AND PERIODIC WAVE SOLUTIONS OF NONLINEAR WAVE EQUATIONS , 2001 .

[9]  Abdul-Majid Wazwaz,et al.  A reliable modification of the Adomian decomposition method for higher-order nonlinear differential equations , 2013, Kybernetes.

[10]  I. Podlubny.  Fractional differential equations , 1998 .

[11]  Abdul-Majid Wazwaz.  On the nonlocal Boussinesq equation: Multiple-soliton solutions , 2013, Appl. Math. Lett..

[12]  Anjan Biswas,et al.  Soliton solutions of Burgers equations and perturbed Burgers equation , 2010, Appl. Math. Comput..

[13]  Milos B. Zivanov,et al.  Symbolic computation of some new nonlinear partial differential equations of nanobiosciences using modified extended tanh-function method , 2011, Appl. Math. Comput..

[14]  Marko D. Petkovic,et al.  Soliton solutions of a few nonlinear wave equations , 2010, Appl. Math. Comput..

[15]  M. Zivanov,et al.  Solitonic Ionic Currents Along Microtubules , 2010 .

[16]  Anjan Biswas,et al.  1-Soliton solution and conservation laws for the Jaulent-Miodekequation with power law nonlinearity , 2010, Appl. Math. Comput..

[17]  Muhammad Younis,et al.  Travelling Wave Solutions of Fractional Order Coupled Burgers' Equations by ( ' ) ⁄ -Expansion Method , 2013 .

[18]  Abdul-Majid Wazwaz,et al.  Adomian decomposition method for solving the Volterra integral form of the Lane-Emden equations with initial values and boundary conditions , 2013, Appl. Math. Comput..

[19]  Anjan Biswas,et al.  1-Soliton solution of the coupled KdV equation and Gear-Grimshaw model , 2010, Appl. Math. Comput..

[20]  Qi Wang,et al.  Numerical solutions for fractional KdV-Burgers equation by Adomian decomposition method , 2006, Appl. Math. Comput..

[21]  R. S. Johnson.  A non-linear equation incorporating damping and dispersion , 1970, Journal of Fluid Mechanics.

[22]  Anjan Biswas,et al.  1-Soliton solution and conservation laws of the generalizedDullin-Gottwald-Holm equation , 2010, Appl. Math. Comput..

[23]  B. Duffy,et al.  An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations , 1996 .

[24]  Anjan Biswas,et al.  1-Soliton solution of the generalized KP equation with generalized evolution , 2010, Appl. Math. Comput..

[25]  M. Younis,et al.  Exact Solution to Nonlinear Differential Equations of Fractional Order via (G’/G)-Expansion Method , 2014 .

[26]  Anjan Biswas,et al.  1-Soliton solution of the generalized KdV equation with generalized evolution , 2010, Appl. Math. Comput..

[27]  Abdul-Majid Wazwaz,et al.  One and two soliton solutions for the sinh-Gordon equation in (1+1), (2+1) and (3+1) dimensions , 2012, Appl. Math. Lett..

[28]  Abdul-Majid Wazwaz,et al.  Dark solitons for a combined potential KdV and Schwarzian KdV equations with t-dependent coefficients and forcing term , 2011, Appl. Math. Comput..