WebApr 26, 2016 · They construct the solution of the Harry-Dym equation via the solution of a 2 × 2 matrix Riemann-Hilbert problem in the complex plane. Further, one-cusp soliton solution is expressed in terms of the Riemann-Hilbert problem. Download to … Webnegative integer flows. Furthermore, in these systems of equations, the dispersive term in the equation is nonlinear, unlike the KdV equation where the dispersive term is linear in the dynamical variable. This is manifest in the structure of the Lax operator and the equation for the Harry Dym equation L = u2∂2, ∂L ∂t = h L3 ≥2,L i, u t ...

An Efficient Approach for Fractional Harry Dym Equation by ... - IJERT

WebAbstract. We describe how the Harry Dym equation fits into the the bi-Hamiltonian formalism for the Korteweg–de Vries equation and other soliton equations. This is achieved using a certain Poisson pencil constructed from two compatible Poisson structures. We obtain an analogue of the Kadomtsev–Petviashivili hierarchy whose reduction leads ... WebThe Korteweg–de Vries (KdV) equation is a mathematical model of waves on shallow water surfaces and it is written as ϕ t + ϕ x x x − 6 ϕ ϕ x = 0. Harry Dym (HD) Equation The nonlinear Dym equation (HD equation, for short) is u t = u 3 u x x x, References Mathematica main page sewage water treatment plant model

Analytic Solutions of Nonlinear Partial Differential Equations by …

WebDec 1, 2024 · The equation (1.1)can be expressed by(ρ2)t−2(1ρ)xxx=0,where ρ=1+q. The problem of Harry Dym equation (1.1)transforms into(1.3)(ρ2)t−2(1ρ)xxx=0,x∈R,t≥0,ρ(x,0)=ρ0(x)=1+q0(x). We assume that the initial value q0(x)in (1.2)satisfies two conditions:(1.4)∫−∞+∞q0(x)dx=0,∫−∞+∞∫±∞xq0(x′)dx′dx=0,x∈R. WebIn this paper, we present a semi-analytic method called the local fractional homotopy analysis method (LFHAM) for solving differential equations involving local fractional derivatives based on the local fractional calculus and the homotopy analysis method. sewage workers vaccinations