This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u
on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .
It has been a great pleasure for me to have prepared the latest edition of my
book on nonlinear optics. My intrigue in the subject matter of this book is as
strong as it was when the first edition was published in 1992.
The principal changes present in the third edition are as follows: (1) The
book has been entirely rewritten using the SI system of units. I personally
prefer the elegance of the gaussian system of units, which was used in the first
two editions, but I realize that most readers would prefer the SI system, and
the change was made for this reason. (2) In...
ON A SHOCK PROBLEM INVOLVING A NONLINEAR VISCOELASTIC BAR
NGUYEN THANH LONG, ALAIN PHAM NGOC DINH, AND TRAN NGOC DIEM Received 3 August 2004 and in revised form 23 December 2004
We treat an initial boundary value problem for a nonlinear wave equation utt − uxx + K |u|α u + λ|ut |β ut = f (x,t) in the domain 0
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping
Wave-Equation Description of Nonlinear Optical Interactions
Các phương trình sóng cho truyền thông quang học phi tuyến
Chúng ta đã thấy trong chương cuối cùng như thế nào phi tuyến trong phản ứng của một hệ thống vật chất vào một lĩnh vực laser cường độ cao có thể gây ra sự phân cực của môi trường để phát triển các thành phần tần số mới không có mặt trong lĩnh vực bức xạ nhiệt.
ON THE EXISTENCE OR THE ABSENCE OF GLOBAL SOLUTIONS OF THE CAUCHY CHARACTERISTIC PROBLEM FOR SOME NONLINEAR HYPERBOLIC EQUATIONS
S. KHARIBEGASHVILI Received 20 October 2004
For wave equations with power nonlinearity we investigate the problem of the existence or nonexistence of global solutions of the Cauchy characteristic problem in the light cone of the future. 1. Statement of the problem Consider a nonlinear wave equation of the type u := ∂2 u − ∆u = f (u) + F, ∂t 2 (1.1)
where f and F are the given real functions; note that f is a nonlinear and u is an unknown real...
This book is devoted to one of the most interesting and rapidly developing
areas of modern nonlinear physics and mathematics – theoretical, analytical
and numerical, study of the structure and dynamics of one-dimensional as well
as two- and three-dimensional solitons and nonlinear wave packets described
by the Korteweg–de Vries (KdV), Kadomtsev–Petviashvili (KP), nonlinear
Schr¨odinger (NLS) and derivative nonlinear Schr¨odinger (DNLS) classes of
The nonlinear absorption of a strong electromagnetic wave caused by confined electrons in cylindrical quantum wires is theoretically studied by using the quantum kinetic equation for electrons. The problem is considered in the case electron-acoustic phonon scattering. Analytic expressions for the dependence of the nonlinear absorption coefficient of a strong electromagnetic wave by confined electrons in rectangular quantum wires on the temperature T are obtained.