What should one who experiences a wet dream while traveling or on desert journeys and is unable to perform ghusl do?

Whoever is in a state of major ritual impurity (janabah (definition)) must perform ghusl (definition) (ritual bath). If they cannot find water, or fear using it due to extreme cold and cannot find a way to warm it, they are permitted to perform tayammum (definition) (dry ablution) and pray, based on the Almighty’s saying: "And if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and find no water, then seek clean earth and wipe over your faces and your hands [with it]." This is also supported by the story of Amr ibn al-Aas (may Allah be pleased with him) performing tayammum for janabah, fearing perishing due to the cold. However, abandoning ghusl and prayer while in a state of janabah out of shyness or embarrassment is forbidden and a grave evil, and its perpetrator must repent. If the reason for not performing ghusl was the absence of water or its extreme coldness, and they performed tayammum, then their prayer is valid. Otherwise, it is not valid and they must repeat it.