• 제목/요약/키워드: Formal linearization

검색결과 7건 처리시간 0.019초

THE FORMAL LINEARIZATION METHOD TO MULTISOLITON SOLUTIONS FOR THREE MODEL EQUATIONS OF SHALLOW WATER WAVES

  • Taghizadeh, N.;Mirzazadeh, M.;Paghaleh, A. Samiei
    • 충청수학회지
    • /
    • 제25권3호
    • /
    • pp.381-391
    • /
    • 2012
  • In this paper, the formal linearization method is used to construct multisoliton solutions for three model of shallow water waves equations. The three models are completely integrable. The formal linearization method is an efficient method for obtaining exact multisoliton solutions of nonlinear partial differential equations. The method can be applied to nonintegrable equations as well as to integrable ones.

THE MULTISOLITON SOLUTION OF GENERALIZED BURGER'S EQUATION BY THE FORMAL LINEARIZATION METHOD

  • Mirzazadeh, Mohammad;Taghizadeh, Nasir
    • 대한수학회논문집
    • /
    • 제26권2호
    • /
    • pp.207-214
    • /
    • 2011
  • The formal linearization method is an efficient method for constructing multisoliton solution of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, we obtain multisoliton solution of generalization Burger's equation and the (3+1)-dimension Burger's equation and the Boussinesq equation by the formal linearization method.

THE EXACT SOLUTION OF KLEIN-GORDON'S EQUATION BY FORMAL LINEARIZATION METHOD

  • Taghizadeh, N.;Mirzazadeh, M.
    • 호남수학학술지
    • /
    • 제30권4호
    • /
    • pp.631-635
    • /
    • 2008
  • In this paper we discuss on the formal linearization and exact solution of Klein-Gordon's equation (1) $u_{tt}-au_{xx}+bu-cu^3=0 a,b,c{\in}R^+$ So that we know an efficient method for constructing of particular solutions of some nonlinear partial differential equations is introduced.

A formal linearization of nonlinear systems based on the discrete-fourier transform

  • Takata, Hitoshi;Komatsu, Kazuo
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
    • /
    • pp.1823-1827
    • /
    • 1991
  • The problem regarding nonlinear systems has come to occupy an important position. In order to solve a nonlinear problem we have methods of linearization which are developed through linear approximation to adapt linear system theories. In this paper we present a formal linearization of nonlinear systems based on the discrete-Fourier transform (D.F.T.).

  • PDF

An Approach to a Formal Linearization toy Time-variant Nonlinear Systems using Polynomial Approximations

  • Komatsu, Kazuo;Takata, Hitoshi
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 제어로봇시스템학회 2002년도 ICCAS
    • /
    • pp.52.2-52
    • /
    • 2002
  • In this paper we consider an approach to a formal linearization for time-variant nonlinear systems. A time-variant nonlinear sysetm is assumed to be described by a time-variant nonlinear differential equation. For this system, we introduce a coordinate transformation function which is composed of the Chebyshev polynomials. Using Chebyshev expansion to the state variable and Laguerre expansion to the time variable, the time-variant nonlinear sysetm is transformed into the time-variant linear one with respect to the above transformation function. As an application, we synthesize a time-variant nonlinear observer. Numerical experiments are included to demonstrate the validity of...

  • PDF

A formal linearization of nonlinear systems based on the trigonometric fourier expansion

  • Takata, Hitoshi;Komatsu, Kazuo
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
    • /
    • pp.939-942
    • /
    • 1989
  • Most of systems are included nonlinear characteristics in practice. One might be faced with difficulties when problems of nonlinear systems are solved. In this paper we present a formal linearization method of nonlinear systems by using the trigonometric Fourier expansion on the state space considering easy inversion. An error bound, an application, and a compensation of this method are also investigated.

  • PDF

A formal linearization method via cubic splines and its applications

  • Narikiyo, Katsuhiro;Takata, Hitoshi
    • 제어로봇시스템학회:학술대회논문집
    • /
    • 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 22-24 Oct. 1991
    • /
    • pp.1848-1853
    • /
    • 1991
  • To solve the nonlinear system problems, many methods have been proposed. Generally those methods however need long processing time because of their complicated algorithms. On the other hand, some simple linearization methods also have been studied. In this paper, a new linearization method using cubic splines[1] is proposed. The approximated linear system obtained by this method we can apply the conventional simple linear system theories such as Kalman filter[2, 3] for the estimation problem.

  • PDF