Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable app...Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.展开更多
Duffing equation,, has a standard well-known ex-act solution [1]. Approximate solutions to this equation also are available [2]. Reference [3] [4] introduces a sinusoidal time-dependent Power Series solution. Applying...Duffing equation,, has a standard well-known ex-act solution [1]. Approximate solutions to this equation also are available [2]. Reference [3] [4] introduces a sinusoidal time-dependent Power Series solution. Applying this method successfully we investigate the approximate solution of the modified Duffing equations,, for n = 4 and 5. Symbolic manipulative utilities of a Computer Algebra System (CAS) specifically Mathematica [5] extensively is used investigating the results.展开更多
文摘Dissipative soliton resonance (DSR) is a phenomenon where the energy of a soliton in a dissipative system increases without limit at certain values of the system parameters. Using the method of collective variable approach, we have found an approximate relation between the parameters of the normalized complex cubic-quintic Ginzburg-Landau equation where the resonance manifests itself. Comparisons between the results obtained by collective variable approach, and those obtained by the method of moments show good qualitative agreement. This choice also helps to see the influence of the active terms on the resonance curve, so can be very useful in constructing passively mode-locked laser that generate solitons with the highest possible energies.
文摘Duffing equation,, has a standard well-known ex-act solution [1]. Approximate solutions to this equation also are available [2]. Reference [3] [4] introduces a sinusoidal time-dependent Power Series solution. Applying this method successfully we investigate the approximate solution of the modified Duffing equations,, for n = 4 and 5. Symbolic manipulative utilities of a Computer Algebra System (CAS) specifically Mathematica [5] extensively is used investigating the results.
