# include <cmath>
# include <cstdlib>

using namespace std;

# include "sine_gordon_exact.hpp"

//****************************************************************************80

void sine_gordon_exact ( double a, double x, double y, double *u, double *uxy )

//****************************************************************************80
//
//  Purpose:
//
//    sine_gordon_exact() evaluates an exact solution of the Sine-Gordeon PDE.
//
//  Discussion:
//
//    uxy = sin ( u )
//
//    This is a one-soliton solution.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Daniel Arrigo,
//    Analytical Techniques for Solving Nonlinear Partial Differential Equations,
//    Morgan and Clayfoot, 2019,
//    ISBN: 978 168 173 5351.
//
//  Input:
//
//    double A: a parameter.
//
//    double X, Y: the X and Y coordinates of a point.
//
//  Output:
//
//    double *U, *UXY: the values of the solution, and its first 
//    mixed derivative at (X,Y).
//
{
  *u = 4.0 * atan ( exp ( a * x + y / a ) );

  *uxy = 4.0 * ( exp ( a * x + y / a ) - exp ( 3 * a * x + 3 * y / a ) ) 
    / pow ( 1.0 + exp ( 2 * a * x + 2 * y / a ), 2 );

  return;
}
//****************************************************************************80

double sine_gordon_residual ( double u, double uxy )

//****************************************************************************80
//
//  Purpose:
//
//    sine_gordon_residual() evaluates the residual for the Sine-Gordeon PDE.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 May 2024
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Daniel Arrigo,
//    Analytical Techniques for Solving Nonlinear Partial Differential Equations,
//    Morgan and Clayfoot, 2019,
//    ISBN: 978 168 173 5351.
//
//  Input:
//
//    double U, UXY: the values of the solution, and its
//    first mixed derivative.
//
//  Output:
//
//    double R, the residual.
//
{
  double r;

  r = uxy - sin ( u );

  return r;
}