Results 211 to 220 of about 35,653 (239)
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1989
To end this book we shall briefly indicate the application of ill-posed integral equations of the first kind to inverse acoustic scattering problems. Of course, in one single chapter it is impossible to give a comlete picture of inverse scattering. Hence we shall content ourselves with developing some of the main ideas and will leave out much of the ...
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To end this book we shall briefly indicate the application of ill-posed integral equations of the first kind to inverse acoustic scattering problems. Of course, in one single chapter it is impossible to give a comlete picture of inverse scattering. Hence we shall content ourselves with developing some of the main ideas and will leave out much of the ...
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Electromagnetic inverse scattering
1971 Antennas and Propagation Society International Symposium, 1971An Electromagnetic Inverse Scattering Identity, based on the Physical Optics Approximation, is developed for the monostatic scattered far field cross section of perfect conductors. Uniqueness of this inverse identity is proven. This identity requires complete scattering information for all frequencies and aspect angles.
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Journal of Mathematical Physics, 1974
In a previous paper the inverse problem associated with a hyperbolic dispersive partial differential equation with smooth coefficients was considered. The inverse problem (the determination of the coefficients) was formulated in terms of a dual set of integral equations involving measurable quantities, the kernels of the transmission, and reflection ...
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In a previous paper the inverse problem associated with a hyperbolic dispersive partial differential equation with smooth coefficients was considered. The inverse problem (the determination of the coefficients) was formulated in terms of a dual set of integral equations involving measurable quantities, the kernels of the transmission, and reflection ...
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1998
THE FORWARD PROBLEM Consider the eigenvalue problem for the Schrodinger equation $$ \left( {{D^2} + {k^2} + \frac{1}{6}u} \right)\psi = 0 $$ (5.1.1) where u is real and lies in S. S(ℝ) is the class of all C∞ functions on the real line for which $$ \mathop {\sup }\limits_x \left| {{x^m}{D^n}u} \right| < + \infty $$ for all non-negative ...
Carlo Cercignani, David H. Sattinger
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THE FORWARD PROBLEM Consider the eigenvalue problem for the Schrodinger equation $$ \left( {{D^2} + {k^2} + \frac{1}{6}u} \right)\psi = 0 $$ (5.1.1) where u is real and lies in S. S(ℝ) is the class of all C∞ functions on the real line for which $$ \mathop {\sup }\limits_x \left| {{x^m}{D^n}u} \right| < + \infty $$ for all non-negative ...
Carlo Cercignani, David H. Sattinger
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2016
We develop a local version of the inverse scattering method for studying soliton equations of parabolic type (this includes, for example, Korteweg–de Vries, nonlinear Schrodinger, and Boussinesq equations, but not sine-Gordon). The potentials are germs of holomorphic matrix-valued functions, without any boundary conditions.
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We develop a local version of the inverse scattering method for studying soliton equations of parabolic type (this includes, for example, Korteweg–de Vries, nonlinear Schrodinger, and Boussinesq equations, but not sine-Gordon). The potentials are germs of holomorphic matrix-valued functions, without any boundary conditions.
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2009
This chapter contains sections titled: Linear Inverse Problems One-Dimensional Inverse Problems Higher-Dimensional Inverse Problems This chapter contains sections titled: Exercises for Chapter 9 References for Chapter 9 Further Readings for Chapter ...
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This chapter contains sections titled: Linear Inverse Problems One-Dimensional Inverse Problems Higher-Dimensional Inverse Problems This chapter contains sections titled: Exercises for Chapter 9 References for Chapter 9 Further Readings for Chapter ...
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2011
We discuss the results obtained using the inversion and refraction corrected reflection (RFCR) algorithms described in the companion paper in these proceedings. We show images for three patients created with these algorithms, from data collected with our clinical device.
J. Wiskin +6 more
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We discuss the results obtained using the inversion and refraction corrected reflection (RFCR) algorithms described in the companion paper in these proceedings. We show images for three patients created with these algorithms, from data collected with our clinical device.
J. Wiskin +6 more
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Wave Motion, 1984
Several inverse techniques are developed for determining the shape of an unknown scattering surface by analyzing backscattered acoustic or electromagnetic waves. These techniques are based on asymptotic high frequency representations of the fields and may be divided into three categories.
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Several inverse techniques are developed for determining the shape of an unknown scattering surface by analyzing backscattered acoustic or electromagnetic waves. These techniques are based on asymptotic high frequency representations of the fields and may be divided into three categories.
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1982
The method of inverse scattering is a new method of mathematical physics, which is applicable to a class of nonlinear wave equations. This chapter was written by V.E. Zakharov who made a significant contribution to the development of the method.
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The method of inverse scattering is a new method of mathematical physics, which is applicable to a class of nonlinear wave equations. This chapter was written by V.E. Zakharov who made a significant contribution to the development of the method.
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1995
Since Gardner, Greene, Kruskal and Miura (abbr. GGKM) discovered that the integrable system method of the Schrodinger equation can be used to solve the initial value problem of the KdV equation, this new method of solving nonlinear partial differential equations has developed quickly in recent years.
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Since Gardner, Greene, Kruskal and Miura (abbr. GGKM) discovered that the integrable system method of the Schrodinger equation can be used to solve the initial value problem of the KdV equation, this new method of solving nonlinear partial differential equations has developed quickly in recent years.
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