and Applied Analysis 3 From 2.1 , we have ut f ′′ ( φ ) φxφt f ′ ( φ ) φxt u1t, 2.2 ux f ′′ ( φ ) φ2 x f ′φ ) φxx u1x, 2.3 uxx f ′′′ ( φ ) φ3 x 3f ′′φ ) φxφxx f ′ ( φ ) φxxx u1xx, 2.4 u2 ( f ′ )2( φ ) φ2 x 2f ′φxu1 x, t u1 x, t , u3 ( f ′ )3( φ ) φ3 x 3 ( f ′ )2 φ2 xu1 x, t 3f φxu1 x, t u 3 1 x, t . 2.5 Substituting 2.1 – 2.5 into the left side of 1.1 and collecting all terms with φ3 x, we obta...

This paper presents explicit analytical solutions of the pressure coefficient and the pressure ratio across the oblique shock and expansion waves in function of the flow deflection angle. These new explicit pressure-deflection solutions can be efficiently used in solving applied aerodynamic problems in supersonic flows, such as the aerodynamics of airfoils and wings in supersonic-hypersonic flo...

A generalized tanh method has been proposed and discussed. This method has been employed for solving two well-known models of nonlinear equations, namely the Drinfeld-Sokolov (DS) system and PHI-four equation. The exact solutions of these models are obtained. Finally, some wave solutions are exhibited.

In recent years, various direct methods were proposed to find exact solutions not only for nonlinear partial differential equations but also for nonlinear differential-difference equations (NDDEs). In this paper, the Exp-function method was extended to the discrete Burgers equation for searching traveling waves in closed forms. It was shown that the equation supported discrete solitary wave sol...

The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long WaveBurgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker’s parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational for...

Explicit solutions to vertical and horizontal displacements are derived for large deformation of a cantilever beam under point load at the free end by an improved homotopy analysis method (IHAM). Quadratic cubic nonlinear differential equations adopted construct more proficient respectively combined with their currently available displacement equations. Higher-order iterative established solve ...

One of the most important topics in geophysics is to study convection in a sea. Based on the algebraic characteristics of the equations of dynamic convection in a sea, we introduce various schemes with multiple parameter functions to solve these equations and obtain families of new explicit exact solutions with multiple parameter functions. Moreover, symmetry transformations are used to simplif...

We present quantum graphs with remarkably regular spectral characteristics. We call them regular quantum graphs. Although regular quantum graphs are strongly chaotic in the classical limit, their quantum spectra are explicitly solvable in terms of periodic orbits. We present analytical solutions for the spectrum of regular quantum graphs in the form of explicit and exact periodic orbit expansio...

A class of explicit exact solutions of Einstein Yang Mills Chern Simons (EYMCS) theory corresponding to topological solitons carrying non-Abelian topological electric charge is obtained. This verifies a conjecture made in Ref.[1,2] regarding the stabilization of the corresponding charged configurations in the theory without gravity .