Magma is generated by partial melting of rocks and ascends due to its buoyancy in interstitial conduits through the country rock. When the country rock creeps, the magma conduits are deformable. A vertical cylindrical conduit that is deformable with time and space is considered for the present analysis, assuming that both country rock and magma are viscous fluids. Here the fluid representing the country rock has a significantly higher viscosity than magma. This analysis can be generalized to permeable flow with a network of deformable magma paths. The theory gives such a solution that a bulge of magma conduit propagates upward at a constant speed without change of wave form. Such a stationary wave resumes its form after collision with another wave so that it may be called magma soliton. The propagation velocity of a magma soliton increases with increasing amplitude. If magma flux is changed to a higher value at a certain depth, a new state of greater flux is established upward, creating new magma solitons at the moving tip. This process of soliton creation might be applicable for explaining the episodicity of volcanic eruptions.
