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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT 257 34 "Examples for using Conse
rvationLaw" }}{PARA 19 "" 0 "" {TEXT 256 75 "A maple package for the c
omputation of conserved densities and their fluxes" }}{PARA 256 "" 0 "
" {TEXT 258 121 "                                                     \+
                    Authors: Bernard Deconinck and Michael A. Nivala" 
}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Preliminaries" }}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 59 "Change to the directory in which the program fi
le is saved." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart; cu
rrentdir();" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 25 "Read in the progra
m file." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "read(\"conser5.t
xt\");\n" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }
{TEXT 260 8 "Examples" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "No Opti
ons" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "kdv:=[diff(u(x,t),t)+
u(x,t)*diff(u(x,t),x)+diff(u(x,t),x,x,x)];" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "ConservationLaw(kdv,[u(x,t)],x,[8]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "nls:=[diff(u(x,t),t)-I/2*diff(u(x,
t),x,x)-I*u(x,t)^2*v(x,t),diff(v(x,t),t)+I/2*diff(v(x,t),x,x)+I*v(x,t)
^2*u(x,t)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "Conservation
Law(nls,[u(x,t),v(x,t)],x,[3]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 
4 "Flux" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Computing the corespond
ing flux:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "ConservationLa
w(kdv,[u(x,t)],x,[2,4,6],flux);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 48 "ConservationLaw(nls,[u(x,t),v(x,t)],x,[3],flux);" }}}}{SECT 0 
{PARA 3 "" 0 "" {TEXT -1 10 "Parameters" }}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 23 "Introducing parameters:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 257 "mvdnls:=[diff(u(z,t),t)-3*u(z,t)^2*diff(u(z,t),z)-v(
z,t)^2*diff(u(z,t),z)-2*u(z,t)*v(z,t)*diff(v(z,t),z)-Gamma*diff(u(z,t)
,z)+diff(v(z,t),z,z),diff(v(z,t),t)-3*v(z,t)^2*diff(v(z,t),z)-u(z,t)^2
*diff(v(z,t),z)-2*v(z,t)*u(z,t)*diff(u(z,t),z)-diff(u(z,t),z,z)];" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "ConservationLaw(mvdnls,[u(z,
t),v(z,t)],z,[4]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "Conse
rvationLaw(mvdnls,[u(z,t),v(z,t)],z,[4],parameters=[Gamma]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "fkdv:=[diff(u(x,t),t)+u(x,t
)*diff(u(x,t),x,x,x)+a*diff(u(x,t),x)*diff(u(x,t),x,x)+b*u(x,t)^2*diff
(u(x,t),x)+diff(u(x,t),x$5)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 55 "ConservationLaw(fkdv,[u(x,t)],x,[10],parameters=[a,b]);" }}}}
{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Weights" }}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 18 "Providing weights:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "ConservationLaw(kdv,[u(x,t)]
,x,[8],returnweights);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "C
onservationLaw(kdv,[u(x,t)],x,[8],weights=[4],weightx=2);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "ConservationLaw(kdv,[u(x,t)],x,[8],
parameters=[a],weights=[2,1]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 
13 "More Examples" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "E3D:=[
diff(u1(x,t),t)+a1*diff(u1(x,t),x)-b1*u2(x,t)*u3(x,t),diff(u2(x,t),t)+
a2*diff(u2(x,t),x)-b2*u1(x,t)*u3(x,t),diff(u3(x,t),t)+a3*diff(u3(x,t),
x)-b3*u1(x,t)*u2(x,t)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "
ConservationLaw(E3D,[u1(x,t),u2(x,t),u3(x,t)],x,[2],parameters=[a],flu
x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "dsw:=[diff(u(x,t),t
)+p*v(x,t)*diff(v(x,t),x),diff(v(x,t),t)+q*diff(v(x,t),x,x,x)+r*u(x,t)
*diff(v(x,t),x)+s*v(x,t)*diff(u(x,t),x)];" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 62 "ConservationLaw(dsw,[u(x,t),v(x,t)],x,[8],parameter
s=[r,s,p]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "boussinesq:
=[diff(u(x,t),t)+diff(v(x,t),x)+u(x,t)*diff(u(x,t),x)+s*diff(u(x,t),x,
x),diff(v(x,t),t)+diff(u(x,t)*v(x,t),x)+r*diff(v(x,t),x,x)+p*diff(u(x,
t),x,x,x)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Conservation
Law(boussinesq,[u(x,t),v(x,t)],x,[6],parameters=[r,s,p]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{MARK "1 2 0 0" 22 }
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