def main():
# -- DEFINE SIMULATION PARAMETERS
x_max, Nx = np.pi, 512
t_max, Nt = 30.0, 60000
n_skip = 60
P, theta, d2 = 1.37225, 2., -0.002
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
x = np.linspace(-x_max, x_max, Nx, endpoint=False)
k = FTFREQ(x.size, d=x[1] - x[0]) * 2 * np.pi
# ... LUGIATO-LEFEVER MODEL
Lk = lambda k: -(1 + 1j * theta) + 1j * d2 * k * k
Nk = lambda uk: (lambda ut: (FT(1j * np.abs(ut)**2 * ut + P)))(IFT(uk))
# ... SOLVER BASED ON SIMPLE SPLIT-STEP FOURIER METHOD
solver = SiSSM(Lk(k), Nk)
# ... INITIAL CONDITION
u_0k = FT(0.5 + np.exp(-(x / 0.85)**2) + 0j)
solver.set_initial_condition(k, u_0k)
# -- RUN SIMULATION
solver.propagate(z_range=t_max, n_steps=Nt, n_skip=n_skip)
t_, uxt = solver.z, solver.utz
x_lim = (-np.pi, np.pi)
k_lim = (-150, 150)
plot_evolution_LLE(t_, x, uxt, x_lim, k_lim)
def main():
# -- DEFINE SIMULATION PARAMETERS
x_min = 0.
x_max = 2.
Nx = 512
t_min = 0.
t_max = 6.0
Nt = 30000
n_skip = 10
delta = 0.022
# -- INITIALIZATION STAGE
# ... COMPUTATIONAL DOMAIN
x = np.linspace(x_min, x_max, Nx, endpoint=False)
k = FTFREQ(x.size, d=x[1] - x[0]) * 2 * np.pi
# ... KORTEWEG DEVRIES MODEL
Lk = -1j * k * k * k * delta * delta
Nk_fun = lambda uk: 0.5j * k * FT(IFT(uk)**2)
# ... SOLVER BASED ON INTEGRATING FACTOR METHOD
solver = IFM_RK4IP(Lk, Nk_fun)
# ... INITIAL CONDITION
u_0x = np.cos(np.pi * x)
solver.set_initial_condition(k, FT(u_0x))
# -- RUN SIMULATION
solver.propagate(z_range=t_max, n_steps=Nt, n_skip=n_skip)
plot_evolution_KdV(solver.z, x, np.real(solver.utz))
def N(self, uw):
ut = IFT(uw)
return 1j * self.gamma * FT(np.abs(ut)**2 * ut)
def Nw(self, uw):
ut = IFT(uw)
return self._de_alias(1j * self.gamma * FT(np.abs(ut)**2 * ut))