الفهرس 
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Abstract
This thesis deals with problems arising in the study of nonlinear partial di¤erential
equations (PDEs). Many methods have employed for the analytic treatment of the non-
linear partial di¤erential equations. This thesis contains six chapters.
In the introductory chapter one, we survey the methods used to generate exact traveling
wave solutions for the nonlinear partial di¤erential equations.
In chapter two, we apply four di¤erent methods to nd the exact traveling wave solutions
of some nonlinear PDEs. Firstly, we use the extended tanh-function method to construct
the exact traveling wave solutions of the Biswas-Milovic equation with dual-power law
nonlinearity. With the aid of computer algebraic system Maple, both constant and time-
dependent coe¢ cients of the nonlinear Biswas-Milovic equation are discussed. Secondly,
we use the modi ed extended tanh-function method and the Bäcklund transformation of
the Riccati equation to construct the exact traveling wave solutions of the generalized
KdV-mKdV equation with higher-order nonlinear terms. Finally, we use the Bäcklund
transformation of the generalized Riccati equation to construct the exact traveling wave
solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation.
In chapter three, we apply the two variable (G0
G ; 1
G)-expansion method to nd the ex-
act traveling wave solutions of some nonlinear PDEs, namely, the equation of nano-ionic
currents along microtubules (MTs), the higher order nonlinear Klein-Gordon equations,
the higher order nonlinear Pochhammer-Chree equations, the (2+1)-dimensional nonlin-
ear cubicquintic GinzburgLandau equation (CQGLE), the (1+1)-dimensional resonant
nonlinear Schrödingers equation with dual-power law nonlinearity, the (1+1)-dimensional
Schrödinger-Boussinesq system (SB-system), the (2+1)-dimensional hyperbolic nonlinear
Schrödinger (HNLS) equation, the higher order nonlinear Schrödinger equation which de-
scribes the propagation of ultrashort femtosecond pulses in nonlinear optical bers and the
higher order nonlinear Schrödinger equation which describes the propagation of femtosec-
ond pulses in nonlinear optical bers. Exact traveling wave solutions of these nonlinear
PDEs include kink, anti-kink soliton wave solutions, bell and anti-bell soliton wave solu-
tions as well as periodic and rational wave solutions.
In chapter four, we apply di¤erent methods to nd the exact traveling wave solutions of
some nonlinear PDEs. Firstly, we nd the exact traveling wave solutions of the nonlinear
PDE describing pulse narrowing nonlinear transmission lines by using the new Jacobi ellip-
tic function expansion method. Secondly, we nd the exact traveling wave solutions of the
nonlinear PDE governing wave propagation in nonlinear low-pass electrical transmission
lines by using the new Jacobi elliptic function expansion method and a direct method.
Finally, we apply the extended auxiliary equation method to nd the exact Jacobi el-
liptic function solutions for a class of nonlinear Schrödinger-type equations namely, the
nonlinear cubicquintic GinzburgLandau equation, the resonant nonlinear Schrödingers
equation with dual-power law nonlinearity and the nonlinear generalized Zakharov system
of equations. The exact solutions of these nonlinear PDEs include terms of the hyperbolic
or the trigonometric functions when the modulus of the Jacobi elliptic function m ! 1 or
m ! 0 respectively.
In chapter ve, we apply the generalized projective Riccati equations method to nd the
exact traveling wave solutions of some nonlinear PDE. namely, the nonlinear Pochhammer-
Chree equation, the nonlinear generalized Zakharov-Kuznetsov equation, the nonlinear
PDE describing the nonlinear dynamics of MTs as nanobioelectronics transmission lines,
the nonlinear PDE describing the nonlinear dynamics of radial dislocations in MTs, the
nonlineae PDE governing wave propagation in nonlinear low-pass electrical transmission
lines and the nonlinear PDE describing pulse narrowing nonlinear transmission lines. The
exact traveling wave solutions for these nonlinear PDEs include hyperbolic (kink and anti-
kink solitons, bell and anti-bell solitary wave solutions), trigonometric (periodic solutions)
and rational solutions.
In chapter six, we apply two di¤erent methods to nd the exact traveling wave solu-
tions of some nonlinear PDEs. Firstly, we nd the exact traveling wave solutions of
the nonlinear fth-order Kaup-Kupershmidt equation (KK), the nonlinear fth-order Ito
equation, the nonlinear fth-order Caudrey-Dodd-Gibbon equation (CDG), the nonlinear
fth-order Lax equation and the nonlinear fth-order Sawada-Kotera equation (SK) us-
ing the Kudryashov method. Secondly, we nd the exact traveling wave solutions of the
nonlinear seventh-order Sawada-Kotera-Ito equation (SKI), the nonlinear seventh-order
Kaup-Kupershmidt equation (KK) and the nonlinear seventh-order Lax equation using
the modi ed Kudryashov method. The exact traveling wave solutions for these nonlinear
PDEs include bell and anti-bell soliton wave solutions and symmetrical hyperbolic Lucas
functions solutions.
Finally, comparison between our recent results and the well-known results is given. We
end this abstract with the remark that, we have published tweleve papers from this thesis,
see [20,21,24,46,47,48,49,60,61,75,76,121].