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Solitons and the Inverse Scattering Transform

- L. Debnath
- Physics
- 2012

Dispersion and nonlinearity play a fundamental role in wave motions in nature. The nonlinear shallow water equations that neglect dispersion altogether lead to breaking phenomena of the typical… Expand

Introduction to the Theory and Application of the Laplace Transformation

- L. Debnath
- Mathematics, Computer Science
- IEEE Transactions on Systems, Man, and…
- 1 June 1974

Integral Transforms and Their Applications

- L. Debnath, D. Bhatta
- Physics, Mathematics
- 30 September 1995

INTEGRAL TRANSFORMS Brief Historical Introduction Basic Concepts and Definitions FOURIER TRANSFORMS AND THEIR APPLICATIONS Introduction The Fourier Integral Formulas Definition of the Fourier… Expand

Nonlinear Partial Differential Equations for Scientists and Engineers

- L. Debnath
- Mathematics
- 19 August 1997

Partial differential equations (PDEs) originated from the study of geometrical surfaces and a wide variety of problems in mechanics. Since till today they are essential in modeling of natural… Expand

Convergence of Ishikawa Iterates of Quasi-Nonexpansive Mappings

- M. K. Ghosh, L. Debnath
- Mathematics
- 1 March 1997

Abstract This paper deals with a necessary and sufficient condition for the convergence of Ishikawa iterates of quasi-nonexpansive mapping in a Banach space. The convergence of Ishikawa iterates for… Expand

Introduction to Hilbert spaces with applications

- L. Debnath, P. Mikusinski
- Mathematics
- 1990

Normed Vector Spaces The Lebesgue Integral Hilbert Spaces and Orthonormal Systems Linear Operators on Hilbert Spaces Applications: Applications to Integral and Differential Equations Generalized… Expand

Tables of Integral Transforms

- L. Debnath
- Mathematics
- 2012

In this chapter, we provide a set of short tables of integral transforms of the functions that are either cited in the text or are in most common use in mathematical, physical, and engineering… Expand

Nonlinear Water Waves

- L. Debnath
- Physics
- 12 April 1994

Basic Equations of Motion of Inviscid and Viscous Fluids. The Theory of Surface Waves on Water. Transient Wave Motions in an Inviscid Fluid. Nonlinear Shallow Water Waves and Solitons. Ship Waves and… Expand

RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING

- L. Debnath, R. Feynman
- Mathematics
- 2003

This paper deals with recent applications of fractional calculus
to dynamical systems in control theory, electrical circuits with
fractance, generalized voltage divider, viscoelasticity, … Expand

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