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functions/Depth_parameters/Dysthe_space_HONLSparameters.m

-function [h,k,sigma,cg,cp,lambda,nu,alpha,alpha4,beta,gamma,mu,Dys_hilb,muintexp] = Dysthe_HONLSparameters(omega,kh,x,FOD)
-     %%
-    % input params 
-    % omega is the angular frequency in units of g^{1/2}
-    % hk is the current value of h(x)k(x)
-    % x is the position along the propagation distance
-    % 
-    % output params
-    % k(x) wavenumber
-    % sigma = tanh(kh)
-    % cg = group velocity
-    % cp = phase velocity
-    
-    %
-    % The shoaling is trivial, see Djordjevic&Redekopp ZAMP 1978
-    % muintexp is the exp of the integral of mu(x) exp(int(mu))
-    %
-    % The parameters are defined as in Sedletsky JETP Lett. 97, 180-193 (2003)
-    % where the envelope of the surface elevation is used and the expansion
-    % to fourth order is performed
-    %
-    % lambda = group velocity dispersion
-    % alpha = third order dispersion (=0 in the limit of deep water)
-    % alpha4 = fourth order dispersion
-    % nu = cubic nonlinear coefficient
-    % beta = coefficient of |A|^2 D_t A
-    % gamma = coefficient of A D_t |A|^2
-    %
-    % Dysthe according to Debbie's thesis.
-    %%
-    
-  % auxiliary quantities
-%     sigma = tanh(kh);
-%     k = omega.^2./sigma;
-	sigma=1;
-	h=1000;
-	g=1;
-	k = omega.^2;
-%     h = kh.*sigma./omega^2;
-    % group and phase speed
-    cp = omega./k;
-    cg = 0.5.*cp;
-    
-	
-	Dys_hilb=2*k.^3/omega;
-	
-    % nu in the paper
-    sigma2 = (2*omega*cg).^2 - 4 .* kh .* sigma;
-    sigmaq = sigma.^2-1;
-    % mu in the paper
-    sigma3 = sigmaq.^2.*kh - sigma.*(sigma.^2-5);
-    % NLS quantities
-    % beta''/2 = omega''/Cg^3/2
-    lambda = omega./(8.*k.^2); %checked
-    
-    % THIS FORMULA IS NOT CORRECT!!!
-    % alphaT = -omega'''/6
-    % changing to space evolution
-    % TOD
-    % beta3/6 = alphaT/cg^4 - 2*lambda^2*cg   
-    
-    % FOD
-    % beta4/24
-    % TBC
-    % TBC !!!!!!!
-    if FOD ~=0
-        alpha4 = -1./(3*128*omega.^7.*cg.^7).*h.*sigmaq.*(...
-            - 3*kh.^4.*sigmaq.^4.*(1-5.^kh)  ...
-            - 4.*kh.^sigma.^3.*sigmaq.*(1-kh.*sigma).*(3-4*kh.*sigma).*(5-8.*kh.*sigma)...
-            - 4.*kh.^3.*sigma.*sigmaq.^3.*(15+kh.*sigma.*(-31+24.*kh.*sigma))...
-            + sigma.^4.*(-3 + kh.*sigma.*(39+8.*kh.*(-7+2*kh.*sigma)))...
-            + 6.*kh.^2.*sigma.^2.*sigmaq.^2.*(-19+kh.*sigma.*(51+4*kh.*sigma.*(-11 + 4.*kh.*sigma))));
-    else 
-        alpha4 = zeros(size(kh));
-    end
-    % cubic nonlinearity
-    nu =  (omega.*k.^2)./2;
-	beta=3.*(omega.*k)./2;
-	gamma=(omega.*k)./4;
-	
-	
-	% shoaling (depth-related loss/amplification)    
-    mu = (1-sigma.^2).*(1-kh.*sigma)./(sigma+kh.*(1-sigma.^2));
-    muintexp = ((2.*kh + sinh(2*kh))./cosh(kh).^2).^0.5;
-	alpha = 0;
-% 	lambda = lambda.*ON_OFF_coef(1);
-% 	nu = nu.*ON_OFF_coef(2);
-% 	alpha = alpha.*ON_OFF_coef(3);
-%     beta = beta.*ON_OFF_coef(4);
-%     gamma = gamma.*ON_OFF_coef(5);
-
-   
-end
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