Novel anlytical solution to the damped Kawahara equation and its application for modeling the dissipative nonlinear structures in a fluid medium

On Reduce Differential Transformation Method for Solving Damped Kawahara Equation

“…where Q � 105β 2 /169αc and W � ����� 52c/β 􏽰 , and the exact solution of this equation as follows [13]:…”

“…Because there is damping term in the Kawahara equation, the energy of the soliton is not conserved and decays with increasing both c and t, (2) is nonintegrable Hamiltonian system. We consider damped Kawahara (2) with α � 3, β � 0.2, c � 0.4 and subject to the IC [13]. Since we do not have exact solution, we can use the initial condition of Kawahara equation as initial condition of the damped Kawahara [13].…”

“…We consider damped Kawahara (2) with α � 3, β � 0.2, c � 0.4 and subject to the IC [13]. Since we do not have exact solution, we can use the initial condition of Kawahara equation as initial condition of the damped Kawahara [13].…”

“…where α, β, and c are constants. e KE has been solved analytically and numerically in many researches [12][13][14]. e obtained solutions are N-soliton solutions [15], various solitons solutions [16], soliton and breathers [17], and different types of N-soliton and lump solutions [18].…”

Semi-analytical solution of non-homogeneous Duffing oscillator equation by the Padé differential transformation algorithm

“…1–6 One of these significant equations is called the Duffing oscillator equation which is utilized in many sciences such as physics and engineering. 7,8 It was discovered in 1918 by electrical engineer Ger man Duffing. 9 The general form of Duffing equation 10 is given by the following formand it subjects to following initial conditions (ICs)where α , β , γ , w and z are real constants.…”