Self-Similarity and Beyond: Exact Solutions of Nonlinear Problems (Hardcover)

INTRODUCTION
FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS
Linear Partial Differential Equations of First Order
Quasilinear Partial Differential Equation of First Order
Reduction of ut = unux+H(x,t,u)=0 to form Ut + UnnUx=0
Initial Value problem for ut+ g(u)Ux+lh(u)=0
Initial Value problem for ut+ ua+ux+ lub=0
EXACT SIMILARITY SOLUTIONS OF NONLINEAR PDES
Reduction of PDEs by Infinitesimal Transformation
System of Partial Differential Equations
Self-Similar Solutions of the Second Kind-Viscous Gravity Currents
A Nonlinear Heat Equation in Three Dimensions
Similarity Solution of Burgers Equation by Direct Method
Exact Free Surface Flows for Shallow Water Equations via Direct Similarity Approach
Multi-Pronged Approach to Exact Solutions of Nonlinear PDEs-An Example from Gas Dynamics
EXACT TRAVELLING WAVE SOLUTIONS
Travelling Waves Solutions
Simple Waves in 1-D Gas Dynamics
Elementary Nonlinear Diffusive Travelling Waves
Travelling Waves for Higher Order Diffusive Systems
Simple Wave Flows in Multi-Dimensional Systems of Homogeneous Partial Differential Equations
Travelling Waves for Nonhomogeneous Hyperbolic or Dispersive Systems
Exact Hydromagnetic Travellng Waves
Exact Simple Waves on shear Flows in a Copressible Barotropic Medium
EXACT LINEARIZATION OF NONLINEAR PDES
Introduction
Comments on the Solution of Linear PDEs
Burgers Equation in One and Higher Dimensions
Nonlinear Degenerate Diffusion Equation ut=[f(u)ux-1
One-Dimensional Motion of an Ideal Compressible Isentropic Gas in the Hodograph Plane
Born-Infeld Equation
Water Waves up a Uniformly Sloping Beach
Simple Waves on Shear Flows
C-Integrable Nonlinear PDEs
NONLINEARIZATION AND EMBEDDING OF SPECIAL SOLUTIONS
Introduction
Exact Nonlinearization of N Wave Solutions for Generalised Burgers Equations
Burgers Equation in Cylindrical Coordinates with Axisymetry
Nonplanar Burgers Equation-A Composite Solution
Modified Burgers Equation
Embedding of Similarity Solution in a Larger Class
ASYMPTOTIC SOLUTION BY BALANCING ARGUMENTS
Asymptotic Solution by Balancing Arguments-Examples from ODEs
Asymptotic Solution of Nonplanar Burgers Equation with N Wave Initial Conditions
Asymptotic Profiles with Finite Mass in 1-D Contaminant Transport through Porous Media
SERIES SOLUTIONS OF NONLINEAR PDES
Introduction
Analysis of Expansion of a Gas Sphere (Cylinder) into Vacuum
Collapse of a Spherical or cylindrical Cavity
Converging shock Wave from a Spherical or cylindrical Piston

Asymptotic Solutions by Balancing Arguments