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In this article we study the following nonlinear Schrodinger equation iut=Δu−g∣u∣p−1u in a domain Ω⊂Rn with initial condition u(x,0)=ϕ(x) and the Dirichlet boundary condition u(x,t)=Q(x,t) on ∂Ω,… (More)

- Charles Bu
- 1995

In this article the existence of generalized solutions to the modified Korteweg–de Vries equation ut−6σu2ux+uxxx=0 is studied. The solutions are found in certain algebras of new generalized functions… (More)

Abstract We consider a nonlinear Schrodinger equation in a domain Ω ⊂ R n with the inhomegeneous Dirichlet boundary condition u = Q where Q is a given smooth function. The nonlinear term contributes… (More)

- Hongjun Gao, Xiaohua Gu, Charles Bu
- 2007

Abstract The Ginzburg–Landau equation has been used as a simplified mathematical model for various pattern formation systems in mechanics, physics and chemistry. In this paper, we study a generalized… (More)

- Charles Bu
- 1995

- Hongjun Gao, Charles Bu
- Applied Mathematics and Computation
- 2003

A mathematical model of tumor growth governed by diffusion equation is studied where the source of mitotic inhibitor is almost periodic and time-dependent within the tissue. Existence and uniqueness… (More)

- Charles Bu
- 2000

- Hongjun Gao, Charles Bu
- 2004

Abstract We study the following complex Ginzburg–Landau equation with cubic nonlinearity on Ω⊂ R n for t>0 : u t =(a+iα) Δ u−(b+iβ)|u| 2 u (a,b>0) under initial and Dirichlet boundary conditions u (… (More)

- Charles Bu
- 1992

Abstract This paper establishes existence and uniqueness of the weak solution to the Ginzburg-Landau equation posed in a finite domain Ω = [0, L ] for t ⩾ 0, with certain initial-boundary data.

- Hongjun Gao, Charles Bu
- Applied Mathematics and Computation
- 2007

Abstract We study the following Neumann inhomogeneous boundary value problem for the complex Ginzburg–Landau equation on Ω ⊂ R n ( n ⩽ 3 ) : u t = ( a + i α ) Δ u - ( b + i β ) | u | 2 u ( a , b , t… (More)